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

Khadijeh Sadri; David Amilo; Evren Hinçal; Kamyar Hosseini; Soheil Salahshour

doi:10.1016/j.heliyon.2024.e27260

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

Heliyon. 2024 Mar 4;10(5):e27260. doi: 10.1016/j.heliyon.2024.e27260. eCollection 2024 Mar 15.

Authors

Khadijeh Sadri^{1

2

3}, David Amilo^{1

2

3}, Evren Hinçal^{1

2

3}, Kamyar Hosseini^{1

2

3

4}, Soheil Salahshour^{5

6

7}

Affiliations

¹ Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey.
² Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey.
³ Faculty of Art and Science, University of Kyrenia, Kyrenia, TRNC, Mersin 10, Turkey.
⁴ Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
⁵ Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey.
⁶ Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey.
⁷ Faculty of Science and Letters, Piri Reis University, Tuzla, Istanbul, 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.

Keywords: 34K28; 41A30; 45D05; Chebyshev polynomials of the fifth kind; Error bound; Pseudo-operational matrix of integration; Volterra integro-partial differential equations.