Galerkin Method for Nonlinear Volterra-Fredholm Integro-Differential Equations Based on Chebyshev Polynomials

Mostafa, M.; A. M. A, Hesham; Abbas, W.; Fathy, Mohamed

doi:10.21608/erj.2021.177344

Galerkin Method for Nonlinear Volterra-Fredholm Integro-Differential Equations Based on Chebyshev Polynomials

Document Type : Original Article

Authors

¹ Physics and engineering mathematics department, Helwan University, Cairo, Egypt.

² Basic and applied science department, college of engineering and technology, Arab academy for science, technology and maritime transport, Cairo, Egypt.

10.21608/erj.2021.177344

Abstract

We aim in this paper to develop a new algorithm for approximating the analytic solution for the integrodifferential
equations using the Galerkin method. The bases of the solution obtained by the proposed algorithm
are Chebyshev polynomials. Meanwhile, some theorems are deducted to simplify the nonlinear algebraic set
resulted from applying the Galerkin method, while Newton's method is used to solve the resulting nonlinear
algebraic system. Examples are introduced to prove the effectiveness of this algorithm in comparison with some
other methods.

Keywords