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Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices

Author

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

Abstract

In this paper, we propose and analyze an efficient matrix method based on shifted Legendre polynomials for the solution of non-linear volterra singular partial integro-differential equations(PIDEs). The operational matrices of integration, differentiation and product are used to reduce the solution of volterra singular PIDEs to the system of non-linear algebraic equations. Some useful results concerning the convergence and error estimates associated to the suggested scheme are presented. illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:310-321
    DOI: 10.1016/j.amc.2016.11.012
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. 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).
    3. 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.
    4. Devi, Vinita & Maurya, Rahul Kumar & Singh, Somveer & Singh, Vineet Kumar, 2020. "Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 367(C).

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    3. 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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