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

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  • Firoozjaee, M.A.
  • Yousefi, S.A.

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.

Suggested Citation

  • Firoozjaee, M.A. & Yousefi, S.A., 2018. "A numerical approach for fractional partial differential equations by using Ritz approximation," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 711-721.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:711-721
    DOI: 10.1016/j.amc.2018.05.043
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    References listed on IDEAS

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    1. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    2. Momani, Shaher, 2005. "An explicit and numerical solutions of the fractional KdV equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(2), pages 110-118.
    3. Chuanzhi Bai, 2010. "Existence of Positive Solutions for a Functional Fractional Boundary Value Problem," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-13, June.
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    1. H. Çerdik Yaslan, 2021. "Numerical solution of the nonlinear conformable space–time fractional partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 407-419, June.
    2. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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