Numerical solution of integro-differential equations of high order by wavelet basis, its algorithm and convergence analysis

In the present paper, an attempt was made to develop a numerical method for solving a general form of two-dimensional nonlinear fractional integro-differential equations using operational matrices. Our approach is based on the hybrid of two-dimensional block-pulse functions and two-variable shifted Legendre polynomials. Error bound and convergence analysis of the proposed method are discussed. We prove that the order of convergence of our method is O(1 2 2M−1 N M M!). The presented method is tested by seven test problems to demonstrate the accuracy and computational efficiency of the proposed method and to compare our results with other well-known methods. The comparison highlighted that the proposed method exhibits superior performance than the existing methods, even using a few numbers of bases.

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Operational matrices based on hybrid functions for solving general nonlinear two-dimensional fractional integro-differential equations

Maleknejad

Rashidinia

Eftekhari

2020

Comp. Appl. Math.

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Boubaker Matrix Polynomials and Nonlinear Volterra-Fredholm Integro-differential Equations

Beni¹

2022

Iran J Sci Technol Trans Sci

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A new algorithm for the solution of nonlinear two-dimensional Volterra integro-differential equations of high-order

Wang

Ezz-Eldien

Aldraiweesh

2020

Journal of Computational and Applied Mathematics

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Numerical solution of integro-differential equations of high order by wavelet basis, its algorithm and convergence analysis

Cited by 4 publications

References 9 publications

Operational matrices based on hybrid functions for solving general nonlinear two-dimensional fractional integro-differential equations

Operational matrices based on hybrid functions for solving general nonlinear two-dimensional fractional integro-differential equations

Boubaker Matrix Polynomials and Nonlinear Volterra-Fredholm Integro-differential Equations

A new algorithm for the solution of nonlinear two-dimensional Volterra integro-differential equations of high-order

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