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An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations

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  • Behera, S.
  • Ray, S. Saha

Abstract

In this article, we introduce an operational matrix scheme based on two-dimensional wavelets for the Volterra weakly singular nonlinear partial integro-differential equations. By implementing two-dimensional wavelets approximations and its operational matrices of integration and differentiation along with collocation points, the weakly singular partial integro-differential equations are reduced into the system of nonlinear algebraic equations. Moreover, Bernoulli wavelet approximation and Legendre wavelet approximation have been used for inspecting the errors and convergence analysis of the given problems. Some numerical examples are included to establish the accuracy of the proposed scheme via Bernoulli wavelet approximation and Legendre wavelet approximation respectively. Additionally, comparisons of error values between the two wavelets have been presented.

Suggested Citation

  • Behera, S. & Ray, S. Saha, 2020. "An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307635
    DOI: 10.1016/j.amc.2019.124771
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    References listed on IDEAS

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    1. Zogheib, Bashar & Tohidi, Emran, 2016. "A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 1-13.
    2. Postnikov, Eugene B. & Lebedeva, Elena A. & Lavrova, Anastasia I., 2016. "Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 128-136.
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    Cited by:

    1. Singh, P.K. & Saha Ray, S., 2023. "An efficient numerical method based on Lucas polynomials to solve multi-dimensional stochastic Itô-Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 826-845.
    2. Behera, S. & Saha Ray, S., 2022. "Two-dimensional wavelets scheme for numerical solutions of linear and nonlinear Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 332-358.

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