Sadri, KhadijehSalahshour, SoheılAmilo, DavidHincal, EvrenHosseini, KamyarSalahshour, Soheil2024-05-252024-05-25202412405-84402405-844010.1016/j.heliyon.2024.e272602-s2.0-85187009602https://doi.org/10.1016/j.heliyon.2024.e27260Amilo, David Ikechukwu/0000-0003-0206-2689; Sadri Khatouni, Khadijeh/0000-0001-6083-9527; Hosseini, Kamyar/0000-0001-7137-1456Volterra 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.eninfo:eu-repo/semantics/openAccessChebyshev polynomials of the fifth kindPseudo-operational matrix of integrationVolterra integro-partial differential equationsError boundArticleQ2Q1105WOS:00122160930000138562493