Author
Ahmad Shahsavaran
Bio: Ahmad Shahsavaran is an academic researcher from Islamic Azad University. The author has contributed to research in topics: Nonlinear system & Integral equation. The author has an hindex of 5, co-authored 13 publications receiving 181 citations.
Papers
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TL;DR: A computational method for solving nonlinear Fredholm integral equations of the second kind which is based on the use of Haar wavelets is presented, which shows efficiency of the method.
154 citations
01 Jan 2011
TL;DR: This work presents a computational method for solving Volterra integral equations of the second kind with weakly singular kernel which is based on the use of Haar wavelets and properties of Block-PulseFunctions (BPF).
Abstract: In this work, we present a computational method for solving Volterra integral equations of the second kind with weakly singular kernel which is based on the use of Haar wavelets and properties of Block-PulseFunctions(BPF). Error analysis is worked out that shows efficiency and the order of convergence of the method. Finally, we also give some numerical examples.
9 citations
01 Jan 2011
TL;DR: In this paper, a numerical method for solving nonlinear Fredholm-Volterra integral equations is presented, which is based upon Lagrange functions approximations and Gaussian quadrature rule.
Abstract: A numerical method for solving nonlinear Fredholm-Volterra integral equations is presented. The method is based upon Lagrange functions approximations. These functions together with the Gaussian quadrature rule are then utilized to reduce the Fredholm-Volterra integral equations to the solution of algebraic equations. Some examples are included to demonstrate the validity and applicability of the technique.
8 citations
01 Jan 2012
TL;DR: In this article, a numerical method for solving nonlinear Fredholm integro differential equations of the second kind is presented, which is based upon Lagrange functions approximation and quadrature rule and collocation points are utilized to reduce the main problem to nonlinear system of algebraic equations.
Abstract: A numerical method for solving nonlinear Fredholm integro differential equations of the second kind is presented. The method is based upon Lagrange functions approximation. Quadrature rule and collocation points are utilized to reduce the main problem to nonlinear system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
7 citations
TL;DR: A computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Block-Pulse functions (BPfs) expansion is presented.
Abstract: In this work, we present a computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Block-Pulse functions (BPfs) expansion. Error analysis is worked out that shows efficiency of the method. Finally, we also give some numerical examples.
7 citations
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TL;DR: The Haar wavelet operational matrix is derived and used to solve the fractional order differential equations including the Bagley-Torvik, Ricatti and composite fractional oscillation equations.
250 citations
TL;DR: In this paper, a numerical scheme based on the Haar wavelet operational matrices of integration for solving linear two-point and multi-point boundary value problems for fractional differential equations is presented.
123 citations
TL;DR: The advantage of the proposed new algorithms based on Haar wavelets is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations.
117 citations
TL;DR: An efficient direct solver for solving numerically the high-order linear Fredholm integro-differential equations (FIDEs) with piecewise intervals under initial-boundary conditions is developed.
96 citations
TL;DR: A quadrature rule based on uniform Haar wavelets and hybrid functions is proposed to find approximate values of definite integrals for double, triple and improper integrals.
Abstract: A quadrature rule based on uniform Haar wavelets and hybrid functions is proposed to find approximate values of definite integrals. The wavelet-based algorithm can be easily extended to find numerical approximations for double, triple and improper integrals. The main advantage of this method is its efficiency and simple applicability. Error estimates of the proposed method alongside numerical examples are given to test the convergence and accuracy of the method.
86 citations