فهرس المقالات Collocation method

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  1 - تعیین جواب بهینه معادله ی کوپر- اشمیت با پیاده سازی روش های بسط پایه های ژاکوپی و ایرفویل
  شادان صدیق بهزادی فاطمه گروه‌ای علی رفیعی
  در این مقاله، معادله ی کوپر اشمیت را به روش هم محلی با پایه های ژاکوپی و ایرفویل، حل می کنیم. این معادله PDE یکی از معادلات مهم و پرکاربرد در فیزیک و شیمی است. این معادله غیرخطی درمهندسی مکانیک به صورت پدیده موج ظاهر شده، و در فیزیک پلاسما درباره سیستم‌هایی بحث می‌کند أکثر

  در این مقاله، معادله ی کوپر اشمیت را به روش هم محلی با پایه های ژاکوپی و ایرفویل، حل می کنیم. این معادله PDE یکی از معادلات مهم و پرکاربرد در فیزیک و شیمی است. این معادله غیرخطی درمهندسی مکانیک به صورت پدیده موج ظاهر شده، و در فیزیک پلاسما درباره سیستم‌هایی بحث می‌کند که از ذرّات باردار مثبت و منفی تشکیل شده‌اند و می‌توانند آزادانه حرکت کنند. مقایسه سطح تولیدات گرم الکترون و سطح آن باعث انتشار هارمونیک برخی از نشانه های منشاء می شود والکترون های گرما در پلاسما، به صورت کروی تابش می شوند [1]. معادله کوپر- اشمیت نقش مهمی در پراکندگی غیر خطی موج ایفا می کند. امواج انفرادی در پراکندگی غیر خطی رسانه ها پخش می شوند. این امواج یک فرم پایدار را حفظ می کنند. به دلیل تعادل پویا وغیر خطی بودن این معادله راه حل تقریبی در بسیاری از مقالات ارائه شده است [12و13].در این مقاله با پیاده سازی روش های عددی روی معادله مورد نظر، دستگاههای غیر خطی حاصل می شود که می توان آنها را با روش های حل دستگاههای غیرخطی، مثل روش تکراری نیوتن حل کرد. وجود، یکتایی جواب و همگرایی روشها مورد بررسی قرار می گیرد و در مثالی نشان خواهیم داد که با تکرار کم به معیار توقف |u_(n+1)-u_n |/|u_n | تفاصيل المقالة
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  2 - روشی عددی برای حل معادلات انتگرال دو بعدی فردهلم خطی به کمک پایه‌های چندجمله‌ای بوبکر
  فرشاد مهدی فر علی خانی
  در این مقاله، روش هم‌محلی جدیدی، بر مبنای چندجمله‌ای‌های بوبکر، برای جواب‌های تقریبی رده‌ای از معادلات انتگرال دو بعدی فردهلم خطی نوع دوم معرفی کرده‌ایم. خصوصیات توابع بوبکر دوبعدی بکار گرفته شده است. ماتریس اساسی انتگرال‌گیری به وسیله‌ی نقاط هم‌محلی برای کاهش فرم جواب أکثر

  در این مقاله، روش هم‌محلی جدیدی، بر مبنای چندجمله‌ای‌های بوبکر، برای جواب‌های تقریبی رده‌ای از معادلات انتگرال دو بعدی فردهلم خطی نوع دوم معرفی کرده‌ایم. خصوصیات توابع بوبکر دوبعدی بکار گرفته شده است. ماتریس اساسی انتگرال‌گیری به وسیله‌ی نقاط هم‌محلی برای کاهش فرم جواب معادله‌ی انتگرالی به فرم جوابی از دستگاه معادلات جبری مورد استفاده قرار گرفته است. دقت جواب و تحلیل خطا به طور کاملاً دقیق و ساختاری مورد مطالعه قرار گرفته شده و تاکید شده است که روش پیشنهادی برای انواع معادلات انتگرال دو بعدی فردهلم خطی با هسته‌ی پیوسته از نوع چندجمله‌ای کاملاً دقیق و بدون خطا می‌باشد. از طرف دیگر، کمک گرفتن از نرم‌افزار ریاضی مِیپل باعث شده جوابِ ضرایب چند جمله ای بوبکر بسیار آسان محاسبه شود. همچنین، نتایج روش حاضر را با نتایج سایر روش‌های موجود به جهت ارائه اعتبار، دقت و کارایی تکنیک مورد بررسی و مقایسه قرار داده‌ایم. تفاصيل المقالة
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  3 - محاسبه ترازهای انرژی معادلات شرودینگر خطی به روش سینک
  خدیجه نوروزی سید محمد علی آل عمرانی نژاد مهدی سلیمانی بهناز فرنام
  محاسبه انرژی­های معادله شرودینگر در فیزیک از اهمیت ویژه­ای برخوردار است. به عنوان مثال در محاسبه میزان جذب نور و میزان شکست نور در یک ماده، محاسبه انرژی­های گذار بین زیرنواری و انرژی­های گذار بین نواری، از ترازهای انرژی استفاده می­کنیم. همچنین، به کم أکثر

  محاسبه انرژی­های معادله شرودینگر در فیزیک از اهمیت ویژه­ای برخوردار است. به عنوان مثال در محاسبه میزان جذب نور و میزان شکست نور در یک ماده، محاسبه انرژی­های گذار بین زیرنواری و انرژی­های گذار بین نواری، از ترازهای انرژی استفاده می­کنیم. همچنین، به کمک ترازهای­های انرژی می­توان چگالی حالات یک سیستم فیزیکی را یافت و از روی آن به دلیل عایق، نیم رسانا و یا فلز بودن یک ماده پی­برد. روش­های زیادی در خصوص محاسبه ترازهای انرژی وجود دارد که هرکدام از نقاط ضعف و قدرتی برخوردارند. روش­های تکرار مجانبی، الگوریتم ژنتیک، نومروف، شبکه های عصبی، ماتریس انتقال و ... تعدادی از آنها می­باشند. محاسبه ترازهای انرژی به کمک توابع سینک، کمتر مورد توجه دانشمندان این حوزه بوده است. در این مقاله، کارایی روش هم محلی سینک در محاسبه این انرژی­ها را بررسی کرده­ایم. برای حل این مسائل، با استفاده از تقریب تابع مجهول به وسیله توابع سینک و به کمک روش هم محلی، مسئله را به یک مساله ویژه مقداری تبدیل می­کنیم. در ادامه با بیان مثال­هایی، دقت و سرعت این روش را با روش تفاضلات متناهی، که روشی رایج در بین فیزیکدانان است، مقایسه کرده­ایم. درنهایت، با توجه به جداول و محاسبات انجام شده، دقت و سرعت این روش در مقایسه با برخی از روش­ها، ثابت کرده­ایم. تمامی محاسبات با نرم افزار میپل صورت گرفته است. تفاصيل المقالة
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  4 - An Efficient Numerical Method for a Class of Boundary Value Problems, Based on Shifted Jacobi-Gauss Collocation Scheme
  M. Maleki Miyane S. Abbasbandy
  We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomi أکثر

  We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the proposed method. تفاصيل المقالة
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  5 - Numerical ‎S‎olution of a SIR Fractional Model of the Distribution of Computer Viruses Using Dickson Polynomials
  D. Shirani M. Tavassoli ‎Kajani‎ S. Salahshour
  ‎In this paper, a numerical method is presented using a Dickson-based collocations method to solve a fractional model of computer virus propagation. The model presented in this paper is a system of differential equations of fraction. By using the Dickson-based collo أکثر

  ‎In this paper, a numerical method is presented using a Dickson-based collocations method to solve a fractional model of computer virus propagation. The model presented in this paper is a system of differential equations of fraction. By using the Dickson-based collocation method and using Chebyshev's spatial points, we transform the system of deficit differential equations into a system of algebraic equations. In this way, an approximate solution can be found for the proposed model. By introducing the error functions for the expressed fractional model, the accuracy and convergence of the obtained solutions are investigated. Some of the approximate results obtained using this method is displayed in the numerical results ‎section.‎ تفاصيل المقالة
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  6 - A New Efficient Method for Solving System of Fuzzy Volterra Integral Equations Based on Fibonacci ‎Polynomials
  T. Sheverini M. Paripour N. Karamikabir
  10.30495/ijim.2022.19394
  Here, based on the Fibonacci polynomials, a new collocation method is presented in order to solve the system of linear fuzzy Volterra integral equations of the second kind. By using this method, these systems are reduced to a linear system of algebraic equations that ar أکثر

  Here, based on the Fibonacci polynomials, a new collocation method is presented in order to solve the system of linear fuzzy Volterra integral equations of the second kind. By using this method, these systems are reduced to a linear system of algebraic equations that are easily solvable. Also, the existence of the solution and error analysis of the proposed method are discussed. Finally, in order to show the importance and application of the proposed method, we have used several illustrative examples. The method is computationally very attractive and gives very accurate results. Easy implementation and simple operations are the essential features of the Fibonacci polynomials. تفاصيل المقالة
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  7 - The spectral iterative method for Solving Fractional-Order Logistic ‎Equation
  A. Shoja‎ E. Babolian A. R. Vahidi
  In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method \cite{35} and the spectral method. The method أکثر

  In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method \cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numerical method. The solutions obtained are compared with Adomian decomposition method and iterative method used in \cite{35‎} and Adams method \cite{36}.‎ تفاصيل المقالة
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  8 - Solving Volterra's Population Model via Rational Christov Functions Collocation ‎Method
  K. Parand E. ‎Hajizadeh‎ A. Jahangiri S. Khaleqi
  The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integro-differential equation. First, the Volterra's Population Model is converted to a أکثر

  The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integro-differential equation. First, the Volterra's Population Model is converted to a nonlinear ordinary differential equation (ODE), then researchers solve this equation (ODE). The accuracy of method is tested in terms of $RES$ error and compare the obtained results with some well-known results.The numerical results obtained show that the proposed method produces a convergent ‎solution.‎ تفاصيل المقالة
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  9 - Stress Waves in a Generalized Thermo Elastic Polygonal Plate of Inner and Outer Cross Sections
  R Selvamani
  The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane s أکثر

  The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermoelastic plate of polygonal shape, composed of homogeneous isotropic material. The frequency equations are obtained by satisfying the irregular boundary conditions along the inner and outer surface of the polygonal plate. The computed non-dimensional wave number and wave velocity of triangular, square, pentagonal and hexagonal plates are given by dispersion curves for longitudinal and flexural antisymmetric modes of vibrations. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots. تفاصيل المقالة
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  10 - Analysis of Rectangular Stiffened Plates Based on FSDT and Meshless Collocation Method
  Sh Hosseini B Soltani
  In this paper, bending analysis of concentric and eccentric beam stiffened square and rectangular plate using the meshless collocation method has been investigated. For detecting the governing equations of plate and beams, Mindlin plate theory and Timoshenko beam theory أکثر

  In this paper, bending analysis of concentric and eccentric beam stiffened square and rectangular plate using the meshless collocation method has been investigated. For detecting the governing equations of plate and beams, Mindlin plate theory and Timoshenko beam theory have been used, respectively, with the stiffness matrices of the plate and the beams obtained separately. The stiffness matrices of the plate and the beams were combined together using transformation equations to obtain a total stiffness matrix. Being independent of the mesh along with its simpler implementation process, compared to the other numerical methods, the meshless collocation method was used for analyzing the beam stiffened plate. In order to produce meshless shape functions, radial point interpolation method was used where moment matrix singularity problem of the polynomial interpolation method was fixed. Also, the Multiquadric radial basis function was used for point interpolations. Used to have solutions of increased accuracy and stability were polynomials with the radial basis functions. Several examples are presented to demonstrate the accuracy of the method used to analyze stiffened plates with the accuracy of the results showing acceptable accuracy that the employed method in analyzing concentric and eccentric beam stiffened square and rectangular plates. تفاصيل المقالة
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  11 - A novel method to solve fuzzy Volterra integral equations using collocation method
  Nouredin Parandin Mohsen Darabi
  Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introd أکثر

  Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introduced. Some properties of these polynomials are consideredto implement a collocation method in order to approximate the solution of Fuzzy Volterra integral equations ofthe second kind. The existence and uniqueness of the solution also convergence and error analysis of proposedmethod are proved thoroughly. The results showed the calculations of the method are simple and low cost. تفاصيل المقالة
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  12 - Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method
  M. M. Shamivand A. Shahsavaran
  In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.

  In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method. تفاصيل المقالة
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  13 - Application of triangular functions for solving the vasicek model
  Z. Sadati Kh. Maleknejad
  This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic أکثر

  This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and$2m+2$ unknowns. Finally, the error analysis and some numerical examples are providedto demonstrate applicability and accuracy ofthis method. تفاصيل المقالة
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  14 - Bernoulli collocation method with residual correction for solving integral-algebraic equations
  F. Mirzaee
  The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of a أکثر

  The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. Thismethod gives an analytic solution when the exact solutions are polynomials. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. تفاصيل المقالة
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  15 - A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methods
  M. Nili Ahmadabadi H. Laeli Dastjerdi
  In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse m أکثر

  In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radialbasis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it is independent of the geometry of the domain and it does not require any background interpolation or approximation cells. The error analysisof the method is provided. Numerical results are presented, which confirm the theoretical prediction of the convergence behavior of the proposed method. تفاصيل المقالة
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  16 - An efficient method for the numerical solution of functional integral equations
  M. Nili Ahmadabadi
  We propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have bee أکثر

  We propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have been obtained. تفاصيل المقالة
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  17 - Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations
  Khadijeh Sadri Zainab Ayati
  ‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operationa أکثر

  ‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations‎. ‎ Indeed, to solve the system of integro-differential equations, a fast algorithm is used for simplifying the problem under study. ‎The method is applied to solve system of linear and nonlinear Fredholm and Volterra integro-differential equations‎. ‎Illustrative examples are included to demonstrate the validity and efficiency of the presented method‎. It is further found that the absolute errors are almost constant in the studied interval. ‎Also‎, ‎several theorems related to the convergence of the proposed method‎, ‎will be presented‎‎.‎ تفاصيل المقالة
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  18 - Using Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
  Majid Erfanian Sajad Kosari
  Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting أکثر

  Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are applied to find the numerical solution of the linear and nonlinear PDEs. The multiquadric (MQ) RBFs as basis function will introduce and applied to discretize PDEs. Differential quadrature will introduce briefly and then we obtain the numerical solution of the PDEs. DQ is a numerical method for approximate and discretized partial derivatives of solution function. The key idea in DQ method is that any derivatives of unknown solution function at a mesh point can be approximated by weighted linear sum of all the functional values along a mesh line. تفاصيل المقالة
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  19 - The Tau-Collocation Method for Solving Nonlinear Integro-Differential Equations and Application of a Population Model
  Atefeh Armand Zienab Gouyandeh
  This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a sy أکثر

  This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using collocation points, we solve this system and obtain the unknown coefficients. To illustrate the ability and reliability of the method some nonlinear integro-differential equations and population models are presented. The results reveal that the method is very effective and simple. تفاصيل المقالة
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  20 - A Numerical Solution for 2D-Nonlinear Fredholm Integral Equations Based on Hybrid Functions Basis
  Maryam Mohammadi A. Zakeri Majid Karami Narges Taheri Raheleh Nouraei
  10.30495/ijm2c.2023.1960582.1254
  This work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and sol أکثر

  This work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and solved by Newton's iterative method along with the numerical integration and collocation methods. Also, the convergence theorem for this algorithm is proved. Finally, some numerical examples are given to show the effectiveness and simplicity of the proposed method. تفاصيل المقالة
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  21 - SPLINE COLLOCATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS
  A. Lamnii H. Mraoui
  The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique.

  The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique. تفاصيل المقالة
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  22 - SOLVING SINGULAR ODES IN UNBOUNDED DOMAINS WITH SINC-COLLOCATION METHOD
  H. Pourbashash H. Kheiri J. Akbarfam
  Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular p أکثر

  Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability of the sinc-collocation method in overcoming the singular points difficulties makes it an efficient method in dealing with these equations. We use numerical examples to highlight efficiency of sinc-collocation method in problems with singularity in equations. تفاصيل المقالة
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  23 - THE COMPARISON OF EFFICIENT RADIAL BASIS FUNCTIONS COLLOCATION METHODS FOR NUMERICAL SOLUTION OF THE PARABOLIC PDE’S
  S. S. Mirshojaei S. Fayazzadeh
  In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition.

  In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition. تفاصيل المقالة
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  24 - Convergence of collocation Bernoulli wavelet method in solving nonlinear Fredholm integro-differential equations of fractional order
  Abdolali Rooholahi Saeed Akhavan
  We provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional أکثر

  We provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach. We provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach. تفاصيل المقالة
• حرية الوصول المقاله
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  25 - Analysis of Linear Two-Dimensional Equations by Hermitian Meshfree Collocation Method
  محمدامین بهرامی مهرداد فروتن
  Meshfree Collocation Method is used to solve linear two-dimensional problems. This method differs from weak form methods such as Galerkin method and no cellular networking and no numerical integration. Therefore, this method has no constraints such as the integration ac أکثر

  Meshfree Collocation Method is used to solve linear two-dimensional problems. This method differs from weak form methods such as Galerkin method and no cellular networking and no numerical integration. Therefore, this method has no constraints such as the integration accuracy and the integration CPU time, and equations can be isolated directly from the strong form of governing PDE. The fundamental problem of this method is unstable solution especially in the case, including derivative boundary conditions. In this paper hermite type shape functions are used to impose boundary conditions. These shape functions have improved the solution accuracy. also, In this paper effects of various parameters such as type weight functions, order based vector, dilation parameter, distribution nodal on the solution accuracy have been studied. تفاصيل المقالة