A generalized Chebyshev operational method for Volterra integro-partial differential equations with weakly singular kernels

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Date

2024

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Cell Press

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Abstract

Volterra integro-partial differential equations with weakly singular kernels (VIPDEWSK) are utilized to model diverse physical phenomena. A matrix collocation method is proposed for determining the approximate solution of this functional equation category. The method employs shifted Chebyshev polynomials of the fifth kind (SCPFK) to construct two-dimensional pseudooperational matrices of integration, avoiding the need for explicit integration and thereby speeding up computations. Error bounds are examined in a Chebyshev-weighted space, providing insights into approximation accuracy. The approach is applied to several experimental examples, and the results are compared with those obtained using the Bernoulli wavelets and Legendre wavelets methods.

Description

Amilo, David Ikechukwu/0000-0003-0206-2689; Sadri Khatouni, Khadijeh/0000-0001-6083-9527; Hosseini, Kamyar/0000-0001-7137-1456

Keywords

Chebyshev polynomials of the fifth kind, Pseudo-operational matrix of integration, Volterra integro-partial differential equations, Error bound

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1

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Source

Heliyon

Volume

10

Issue

5

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