List of articles (by subject) Numerical Analysis


    • Open Access Article

      1 - Application of the Lie Symmetry Analysis for second-order fractional differential equations
      موسی ایلی جعفر بی آزار زینب آیتی
      Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-o More
      Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach. Manuscript profile
    • Open Access Article

      2 - Improving adaptive resolution of analog to digital converters using least squares mean method
      Shadan Sadigh behzadi
      This paper presents an adaptive digital resolution improvement method for extrapolating and recursive analog-to-digital converters (ADCs). The presented adaptively enhanced ADC (AE-ADC) digitally estimates the digital equivalent of the input signal by utilizing an adapt More
      This paper presents an adaptive digital resolution improvement method for extrapolating and recursive analog-to-digital converters (ADCs). The presented adaptively enhanced ADC (AE-ADC) digitally estimates the digital equivalent of the input signal by utilizing an adaptive digital filter (ADF). The least mean squares (LMS) algorithm also determines the coefficients of the ADF block. In this scheme, the input bandwidth is limited to the Nyquist-rate. This scheme has the ability of enhancing its resolution by one bit through doubling the gain of a low-quality amplifier circuit. Behavioral simulation results are also provided for a 10-bit AE-ADC to verify the usefulness of the approach. Simulation results indicate that the spurious-free dynamic range (SFDR) and signal-to-noise-and-distortion-ratio (SNDR) are 68.8 dB and 55.5 dB, respectively. Manuscript profile
    • Open Access Article

      3 - An efficient technique for solving systems of integral equations
      حمیده ابراهیمی
      In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which More
      In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and at the end, some examples are presented to demonstrate the efficiency and the validity of the proposed method. Manuscript profile
    • Open Access Article

      4 - Shifted Chebyshev Approach for the Solution of Delay Fredholm and Volterra Integro-Differential Equations via Perturbed Galerkin Method
      Kazeem Issa Jafar Biazar Babatunde Yisa
      The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential differen More
      The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered, the new proposed approach performs better than many other methods. Manuscript profile
    • Open Access Article

      5 - A New Eight-Order Iteretive Method for Solving Nonlinear Equations with High Efficiency index
      Waziri Mohammed Yusuf Kabir Saminu
      In this paper, we develop a new eighth-order method for simple roots of non- linear equations via weight function and interpolation methods. The method requires only three(3) function evaluation and a derivative evaluation with 81/4 ≈ 1.682 efficiency index . Nume More
      In this paper, we develop a new eighth-order method for simple roots of non- linear equations via weight function and interpolation methods. The method requires only three(3) function evaluation and a derivative evaluation with 81/4 ≈ 1.682 efficiency index . Numerical comparison between the proposed method with some other methods were presented, which shows that our method is promising . Manuscript profile
    • Open Access Article

      6 - Application of Adomian Decomposition Method and Variational Iteration Method to Dynamical System Problems
      Babatunde Yisa
      Adomian decomposition method and He’s variational Iteration method are applied to nonlinear oscillator problems that involve conservative type of oscillators. The methods proved to be effective for the general and specific cases due to their algorithms that admit More
      Adomian decomposition method and He’s variational Iteration method are applied to nonlinear oscillator problems that involve conservative type of oscillators. The methods proved to be effective for the general and specific cases due to their algorithms that admit nonlinear terms in the problems. The two methods are tested on some specific problems in the literature, and the results obtained compared favourably with those obtained via the use of Energy balance method. Manuscript profile
    • Open Access Article

      7 - Approximate solution of nonlinear fractional order model of HIV infection of CD4+T via Differential Quadrature Radial Basis Functions technique
      کوکب چلمبری حمیده ابراهیمی زینب آیاتی
      In this research, differential quadrature radial basis functions Method is performed to a fractional order model of HIV infection of CD4+T. Here, Caputo fractional derivative is used and it is approximated by forward finite difference method. Results have been compared More
      In this research, differential quadrature radial basis functions Method is performed to a fractional order model of HIV infection of CD4+T. Here, Caputo fractional derivative is used and it is approximated by forward finite difference method. Results have been compared with the results of Laplace Adomian decomposition method (LADM), Laplace Adomian decomposition method-pade (LADM-pade), Runge-Kutta, Variational iteration method (VIM) and Variational iteration method-pade (VIM-Pade) for α_1=α_2=α_3 and residual functions have been plotted. And also approximate solutions of suggested method for different order of fractional derivatives have been shown. Manuscript profile
    • Open Access Article

      8 - 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 More
      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. Manuscript profile
    • Open Access Article

      9 - A BACKWARD DIFFERENTIATION FORMULA FOR THIRD-ORDER INITIAL OR BOUNDARY VALUES PROBLEMS USING COLLOCATION METHOD
      GAFAR TIAMIYU Abosede COLE KHADEEJAH AUDU
      We propose a new self-starting sixth-order hybrid block linear multistep method using backward differentiation formula for direct solution of third-order differential equations with either initial conditions or boundary conditions. The method used collocation and interp More
      We propose a new self-starting sixth-order hybrid block linear multistep method using backward differentiation formula for direct solution of third-order differential equations with either initial conditions or boundary conditions. The method used collocation and interpolation techniques with three off-step points and five-step points, choosing power series as the basis function. The convergence of the method is established, and three numerical experiments of initial and boundary value problems are used to demonstrate the efficiency of the proposed method. The numerical results in Tables and Figures show the efficiency of the method. Furthermore, the numerical method outperformed the results from existing literature in terms of accuracy as evident in the results of absolute errors produced. Manuscript profile
    • Open Access Article

      10 - Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials
      فرشته صائمی حمیده ابراهیمی محمود شفیعی
      The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operationa More
      The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operational matrices, a system of algebraic equations is derived that can be readily handled through the use of the Newton scheme. The stability, error bound, and convergence analysis of the method are discussed in detail by preparing some theorems. Several illustrative examples are provided formally to show the efficiency of the proposed method. Manuscript profile
    • Open Access Article

      11 - Using nonstandard finite difference methods for solving converted Schrodinger equation to an ODE
      فرنوش ایزدی
      In this work, by introducing a transformation, the nonlinear Schrodinger equation is converted to an ordinary differential equation (ODE). Then, two nonstandard finite difference (NSFD) schemes are constructed for studying the reduced equation. It is shown that the meth More
      In this work, by introducing a transformation, the nonlinear Schrodinger equation is converted to an ordinary differential equation (ODE). Then, two nonstandard finite difference (NSFD) schemes are constructed for studying the reduced equation. It is shown that the methods preserve the positivity and boundedness properties of the original equation and are stable conditionally and consistence. Finally, the results of the methods are compared with each other and also with the results of the standard finite difference scheme at some points. The graphs of the errors of numerical solutions for these schemes are plotted and compared with the exact solutions. Manuscript profile
    • Open Access Article

      12 - Numerical Solution of Fokker-Planck-Kolmogorov Time Fractional Differential Equations Using Haar Wavelet Method and convergence and error analysis
      شعبان محمدی S. Reza Hejazi
      The purpose of this paper is to present an efficient numerical method for finding numerical solutions Fokker-Planck-Kolmogorov time-fractional differential equations. The Haar Wave was the first to be introduced. The Fokker-Planck-Kolmogorov time-fractional differential More
      The purpose of this paper is to present an efficient numerical method for finding numerical solutions Fokker-Planck-Kolmogorov time-fractional differential equations. The Haar Wave was the first to be introduced. The Fokker-Planck-Kolmogorov time-fractional differential equation is converted to the linear equation using the Haar wavelet operation matrix in this technique. This method has the advantage of being simple to solve. The simulation was carried out using MATLAB software. Finally, the proposed strategy was used to solve certain problems. The results revealed that the suggested numerical method is highly accurate and effective when used to Fokker-Planck-Kolmogorov time fraction differential equations. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. Moreover, for the convergence of the proposed technique, inequality is derived in the context of error analysis. Manuscript profile
    • Open Access Article

      13 - Convergence of Triple Accelerated Over-Relaxation (TAOR) Method for M-Matrix Linear Systems
      KHADEEJAH AUDU Yusuph Yahaya Rufus Adeboye Usman Abubakar
      In this paper, we propose some necessary conditions for convergence of Triple Accelerated Over-Relaxation (TAOR) method with respect to $M-$ coefficient matrices. The theoretical approach for the proofs is analyzed through some standard procedures in the literature. Som More
      In this paper, we propose some necessary conditions for convergence of Triple Accelerated Over-Relaxation (TAOR) method with respect to $M-$ coefficient matrices. The theoretical approach for the proofs is analyzed through some standard procedures in the literature. Some numerical experiments are performed to show the efficiency of our approach, and the results obtained compared favourably with those obtained through the existing methods in terms of spectral radii of their iteration matrices. Manuscript profile
    • Open Access Article

      14 - Numerical solution of integro-differential equations via pertubed-Gegenbauer, Jacobi polynomials and Galerkin method
      Kazeem Issa Kazeem Aliu Kazeem Arokoola Kazeem Micah
      In this paper, we proposed perturbed Galerkin method for solving integro-differential equations via shifted Gegenbauer and shifted Jacobi polynomials as approximating polynomials. We use Galerkin method to transform the perturbed integro-differential equation to system More
      In this paper, we proposed perturbed Galerkin method for solving integro-differential equations via shifted Gegenbauer and shifted Jacobi polynomials as approximating polynomials. We use Galerkin method to transform the perturbed integro-differential equation to system of linear algebraic equations and obtained N + 1 linear equations with N +m+2 unknowns. Moreover, with m+1 boundary conditions we obtained N +m+2 algebraic equations which was then solved to obtain the approximate solutions at various values of α and β depending on the orthogonal polynomials, that’s shifted Gegenbauer or shifted Jacobi polynomials. The proposed method was implemented on some selected problems in the literature to validate the effectiveness and the accuracy of the proposed method. Manuscript profile
    • Open Access Article

      15 - An Artificial Neural Network Method to Predict the COVID-19 Cases in Iran
      Meisam Shamsi رضا بابازاده Mohsen Varmazyar
      The sudden emergence of a Coronavirus and its rapid spread due to the globalization factors, especially the airline network, provoked the reaction of countries. Governments attempt to use all available means, including prediction methods, to control the spread of the Co More
      The sudden emergence of a Coronavirus and its rapid spread due to the globalization factors, especially the airline network, provoked the reaction of countries. Governments attempt to use all available means, including prediction methods, to control the spread of the Coronavirus. In this article, we have developed various models based on artificial neural networks, including multi-layer perceptron, radial basis function, and adaptive-network-based fuzzy inference system with different learning algorithms, transfer functions, membership functions, hidden layers, hidden neurons, and kernels. We have identified five factors influencing the Coronavirus outbreak based on the Pearson correlation coefficient approach. These factors are gasoline consumption, internet pressure, number of wedding ceremonies, online transactions, and mask consumption. The accuracy of the developed models is identified by calculating three types of statistical errors, including root mean square error, mean absolute error, and mean absolute percentage error. The results show that the radial basis function model predicts the number of Covid-19 cases for the one month (mid-term) with an accuracy of over 97%. This study provides an efficient approach to predict the number of COVID-19 cases which help policymakers to make strategic decisions, including closing borders, designing supply chains for medical and health equipment, and enacting new laws. Manuscript profile
    • Open Access Article

      16 - 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 More
      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. Manuscript profile
    • Open Access Article

      17 - Optimization of Language Learning with TOPSIS
      ترانه جوانبخت
      The present study focuses on the application of fuzzy sets in the optimization of language learning with TOPSIS. The appropriate consideration of the candidates’ characteristics is an important issue which can affect their language learning. Motivation, learner st More
      The present study focuses on the application of fuzzy sets in the optimization of language learning with TOPSIS. The appropriate consideration of the candidates’ characteristics is an important issue which can affect their language learning. Motivation, learner strategies, perseverance and age are the factors that affect language learning. The hypothesis in this paper was that the difference in the consideration of these factors can affect the individuals’ language learning. In this study, for the first time, the analysis of the candidates’ characteristics of two age categories was performed for the investigation of their impact on language learning. The purpose of this work was to analyze the candidates’ characteristics on the individuals’ language learning. The analysis with a decision making algorithm, TOPSIS, revealed the efficiency of this method. One of the advantages of this study was that the effect of different characteristics of the category members on the categories confusion has made the prediction for the optimization of language learning possible. Another advantage was that the modification of the TOPSIS method with the application of fuzzy disjunction has been efficient to provide an automated decision-making tool for this analysis. The results presented in this paper could be used for the development of algorithms and linguistic tools for the optimization of language learning with artificial intelligence. Manuscript profile
    • Open Access Article

      18 - A NEW APPROACH OF FUZZY NUMBERS WITH DIFFERENT SHAPES AND DEVIATION
      A. Ghanizadeh N. Parandin
      In this paper, we propose a new method for fuzzy numbers. In this method, we assume that Ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. So, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. Then, Mic and Mis More
      In this paper, we propose a new method for fuzzy numbers. In this method, we assume that Ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. So, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. Then, Mic and Mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. Finally, we can obtain ranking index (Mi) that is the convex combination of, Mic and Mis. At the end of paper, in one example, the proposed method is compared with other methods. Manuscript profile
    • Open Access Article

      19 - Application of G'/G-expansion method to the (2+1)-dimensional dispersive long wave equation
      جعفر بی آزار زینب آیتی
      In this work G'/G-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. It is shown that G'/G-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equat More
      In this work G'/G-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. It is shown that G'/G-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation. Manuscript profile
    • Open Access Article

      20 - A method to obtain the best uniform polynomial approximation for the family of rational function
      م.ع فریبرزی عراقی ف. فروزانفر
      In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1on any non symmetric interval [d,e]. Using the obtained approxim More
      In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1for both cases b2-4ac L 0and b2-4ac G 0. Manuscript profile
    • Open Access Article

      21 - Exact solutions for wave-like equations by differential transform method
      ج. بی آزار م. اسلامی
      Differential transform method has been applied to solve many functional equations so far. In this article, we have used this method to solve wave-like equations. Differential transform method is capable of reducing the size of computational work. Exact solutions can als More
      Differential transform method has been applied to solve many functional equations so far. In this article, we have used this method to solve wave-like equations. Differential transform method is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Some examples are prepared to show theefficiency and simplicity of the method. Manuscript profile