Author
H. Khatami
Bio: H. Khatami is an academic researcher from Islamic Azad University. The author has contributed to research in topics: Integral transform & Volterra integral equation. The author has an hindex of 1, co-authored 1 publications receiving 95 citations.
Papers
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TL;DR: The characteristic of Block–Pulse functions is described and it is indicated that through this method a system of Fredholm integral equations can be reduced to an algebraic equation.
99 citations
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TL;DR: The Kronecker convolution product is introduced and expanded to the Riemann-Liouville fractional integral of matrices and several operational matrices for integration and differentiation are studied.
171 citations
TL;DR: A way to solve the fractional differential equations using the Riemann-Liouville fractional integral for repeated fractional integration and the generalized block pulse operational matrices of differentiation are proposed.
Abstract: The Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples.
152 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: By using block pulse functions and their stochastic operational matrix of integration, a stochastically Volterra integral equation can be reduced to a linear lower triangular system, which can be directly solved by forward substitution.
95 citations
TL;DR: An approach for obtaining the numerical solution of the nonlinear Volterra-Fredholm integro-differential (NVFID) equations using hybrid Legendre polynomials and Block-Pulse functions that reduces NVFID equations to a system of algebraic equations, which greatly simplifying the problem.
Abstract: This paper introduces an approach for obtaining the numerical solution of the nonlinear Volterra-Fredholm integro-differential (NVFID) equations using hybrid Legendre polynomials and Block-Pulse functions. These hybrid functions and their operational matrices are used for representing matrix form of these equations. The main characteristic of this approach is that it reduces NVFID equations to a system of algebraic equations, which greatly simplifying the problem. Numerical examples illustrate the validity and applicability of the proposed method.
84 citations