This paper is devoted to studying a computational method for solving multi-term differential equations based on new operational matrix of shifted second kind Chebyshev polynomials. The properties of the operational matrix of fractional integration are exploited to reduce the main problem to an algebraic equation. We present an upper bound for the error in our estimation that leads to achieve the convergence rate of O(M −κ ). Numerical experiments are reported to demonstrate the applicability and efficiency of the proposed method.Mathematics Subject Classification. Primary 26A33; Secondary 65L05.
This paper introduces an approach based on hybrid operational matrix to obtain a numerical scheme to solve fractional differential equations. The idea is to convert the given equations into a system of equations, based on the block-pulse and Legendre polynomials. Also, we employ the Banach fixed-point theorem to analyze the problem on the Banach algebra C[0, b] for some fractional differential equations, which include many key functional differential equations that arise in linear and nonlinear analysis. Keywords Fractional differential equations Á Operational matrix Á Legendre polynomials Á Block-pulse function Á Fixed-point theorem Mathematics Subject Classification 41A30 Á 34A08 Á 26A33 Á 42C10 Á 47H10
In this paper, we state an efficient method for solving the fractional Riccati differential equation.This equation plays an important role in modeling the various phenomena in physics and engineering. Our approach is based on operational matrices of fractional differential equations with hybrid of block-pulse functions and Chebyshev polynomials. Convergence of hybrid functions and error bound of approximation by this basis are discussed. Implementation of this method is without ambiguity with better accuracy than its counterpart other approaches. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.
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