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Operational matrix approach for the solution of partial integro-differential equation

Author

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  • Singh, Somveer
  • Patel, Vijay Kumar
  • Singh, Vineet Kumar

Abstract

In this paper, an effective numerical method is introduced for the treatment of Volterra singular partial integro-differential equations. They are based on the operational and almost operational matrix of integration and differentiation of 2D shifted Legendre polynomials. The methods convert the singular partial integro-differential equation in to a system of algebraic equations. Convergence analysis and error estimates are derived for the proposed method. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Suggested Citation

  • Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2016. "Operational matrix approach for the solution of partial integro-differential equation," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 195-207.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:195-207
    DOI: 10.1016/j.amc.2016.02.036
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    Cited by:

    1. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2019. "A novel Legendre operational matrix for distributed order fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 215-231.
    2. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar & Tohidi, Emran, 2017. "Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 310-321.
    3. Singh, Somveer & Devi, Vinita & Tohidi, Emran & Singh, Vineet Kumar, 2020. "An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.

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