A numerical approach for fractional partial differential equations by using Ritz approximation

M.A. Firoozjaee and S.A. Yousefi

Applied Mathematics and Computation, 2018, vol. 338, issue C, 711-721

Abstract: In this article, Ritz approximation have been employed to obtain numerical solutions of fractional partial differential equations (FPDEs) based on the Caputo fractional derivative. Transforming fractional partial differential equations into optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation using Mathematica7 and we have the coefficients of polynomial expansion. We extensively discuss the convergence of the method. Some numerical examples are presented which illustrate the theoretical results and the performance of the method.

Keywords: Fractional partial differential equations; Caputo fractional derivative; The initial and boundary value fractional problem; Polynomial basis functions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:338:y:2018:i:c:p:711-721

DOI: 10.1016/j.amc.2018.05.043

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