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A generalized Chebyshev operational method for Volterra integro-partial differential equations with weakly singular
Khadijeh Sadri1,2,3, David Amilo1,2,3, Evren Hinçal1,2,3
1Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey.
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 pseudo-operational 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.
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