فهرس المقالات Radial basis functions

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  1 - مدل‌سازی بار رسوب کل رودخانه‌ها با استفاده از شبکه‌های عصبی مصنوعی
  امین فلامکی مهناز اسکندری عبدالحسین بغلانی سید احمد احمدی
  برآورد بار رسوب کل رودخانه ها از مسائل مهم و کاربردی در مدیریت و برنامه ریزی منابع آب است. غلظت رسوب می تواند به روش های مستقیم و یا غیرمستقیم محاسبه شود که معمولاً روش های مستقیم پرهزینه و زمان بر هستند. همچنین بار رسوب کل می تواند به کمک روابط مختلف انتقال رسوب محاسبه أکثر

  برآورد بار رسوب کل رودخانه ها از مسائل مهم و کاربردی در مدیریت و برنامه ریزی منابع آب است. غلظت رسوب می تواند به روش های مستقیم و یا غیرمستقیم محاسبه شود که معمولاً روش های مستقیم پرهزینه و زمان بر هستند. همچنین بار رسوب کل می تواند به کمک روابط مختلف انتقال رسوب محاسبه شود، لیکن به طور معمول کاربرد این روابط نیاز به شرایط معینی داشته و به علاوه در بیشتر موارد نتایج حاصل از آن ها با یکدیگر و با مقادیر اندازه گیری شده متفاوت است. هدف از این پژوهش ارائه روشی بر پایه شبکه های عصبی مصنوعی (ANN) در تخمین بار رسوب کل بود. بدین منظور از دو نوع شبکه عصبی پرسپترون چند لایه (MLP) و توابع پایه شعاعی (RBF) و 200 نمونه، استفاده شد. 75 درصد از داده ها برای آموزش و 25 درصد برای آزمون شبکه ها در نظر گرفته شدند. متغیرهای ورودی مدل ها شامل سرعت متوسط جریان، شیب کف آبراهه، عمق متوسط، عرض آبراهه و قطر میانه ذرات رسوب و خروجی مدل، غلظت رسوب بود. متغیرهای ورودی مرحله به مرحله به شبکه ها اضافه شدند و هر بار نتایج ارزیابی شد تا مناسب ترین مدل تعیین شود. سپس نتایج حاصل از مدل های ANN با پنج معادله معروف انتقال رسوب مقایسه شدند. شاخص‌های آماری نشان داد که دقت شبکه های عصبی به ویژه مدل MLP در تخمین بار رسوب کل با ضریب همبستگی 96/0 بیش از سایر مدل هاست. همچنین مشخص شد که برای افزایش دقت مدل نیاز به آموزش آن با هر دو نوع داده های هیدرولوژیک و رسوب است. رابطه Ackersو White در برآورد مقدار بار رسوب کل بسیار بیش برآورد و سایر روابط، کم برآورد بودند. نتایج این پژوهش نشان داد که مدل های ارائه شده بر پایه شبکه های عصبی با مقادیر رسوب کل مشاهده شده هم خوانی بیشتری دارند و بویژه شبکه MLP می تواند مقدار رسوب را در نقاط پیک به خوبی برآورد نماید. تفاصيل المقالة
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  2 - Meshless RBF Method for Linear and Nonlinear Sobolev Equations
  مهران نعمتی محمود شفیعی حمیده ابراهیمی
  Radial Basis Functions are considered as important tools for scattered data interpolation. Collocation procedure is a powerful technique in meshless methods which is developed on the assumption of radial basis functions to solve partial differential equations in high di أکثر

  Radial Basis Functions are considered as important tools for scattered data interpolation. Collocation procedure is a powerful technique in meshless methods which is developed on the assumption of radial basis functions to solve partial differential equations in high dimensional domains having complex shapes. In this study, a numerical method, implementing the RBF collocation method and finite differences, is employed for solving not only 2-D linear, but also nonlinear Sobolev equations. First order finite differences and Crank-Nicolson method are applied to discretize the temporal part. Using the energy method, it is shown that the applied time-discrete approach is convergent in terms of time variable with order . The spatial parts are approximated by implementation of two-dimensional MQ-RBF interpolation resulting in a linear system of algebraic equations. By solving the linear system, approximate solutions are determined. The proposed scheme is verified by solving different problems and error norms and are computed. Computations accurately demonstrated the efficiency of the suggested method. تفاصيل المقالة
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  3 - Improved solution to nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation by a meshless RBFs method
  مهران نعمتی سیده فائزه تیموری
  In this paper, based on the RBF collocation method and finite differences, a numerical method is proposed to solve nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation. First order finite differences and Crank-Nicolson method are applied أکثر

  In this paper, based on the RBF collocation method and finite differences, a numerical method is proposed to solve nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation. First order finite differences and Crank-Nicolson method are applied to discretize the temporal parts. The spatial parts are approximated by MQ-RBF interpolation which results in a linear system of algebraic equations. Approximate solutions are determined by solving such a system. The proposed scheme is verified by solving some test problems and computing error norms and . Results show the efficiency of the suggested method and the error has been improved. تفاصيل المقالة
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  4 - 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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  5 - The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.
  J. Nazari M. Nili Ahmadabadi H. Almasieh
  In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Ga أکثر

  In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented and results are compared to the analytical solution and Triangular functions (TF), Delta basis functions (DFs), block-pulse functions , sinc fucntions, Adomian decomposition, computational, Haar wavelet and direct methods to demonstrate the validity and applicability of the proposed method. تفاصيل المقالة
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  6 - 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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  7 - Numerical Solution of The Parabolic Equations by Variational Iteration Method and Radial Basis Functions
  Sara Hosseini
  ‎In this work‎, ‎we consider the parabolic equation‎: ‎$u_t-u_{xx}=0$‎. ‎The purpose of this paper is to introduce the method of‎ ‎variational iteration method and radial basis functions for‎ ‎solving this equation‎. ‎ أکثر

  ‎In this work‎, ‎we consider the parabolic equation‎: ‎$u_t-u_{xx}=0$‎. ‎The purpose of this paper is to introduce the method of‎ ‎variational iteration method and radial basis functions for‎ ‎solving this equation‎. ‎Also, the method is implemented to three‎ ‎numerical examples‎. ‎The results reveal‎ ‎that the technique is very effective and simple. تفاصيل المقالة
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  8 - Determination of a Source Term in an Inverse Heat Conduction Problem by Radial Basis Functions
  Muhammad Arghand
  In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) أکثر

  In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (IHCP). The other advantage of the method is that can be applied to the problems with various types of boundary conditions. The results of numerical experiments are presented and compared with analytical solutions. The results demonstrate the reliability and efficiency of the proposed scheme. تفاصيل المقالة