Galerkin Method for Nonlinear Volterra-Fredholm Integro-Differential Equations Based on Chebyshev Polynomials | ||||
| Engineering Research Journal | ||||
| Article 15, Volume 170, Issue 0, June 2021, Page 169-183 PDF (427.29 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/erj.2021.177344 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| M. Mostafa* 1; Hesham A. M. A1; W. Abbas2; Mohamed Fathy2 | ||||
| 1Physics and engineering mathematics department, Helwan University, Cairo, Egypt. | ||||
| 2Basic and applied science department, college of engineering and technology, Arab academy for science, technology and maritime transport, Cairo, Egypt. | ||||
| 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 | ||||
| Integro-differential equations; Chebyshev polynomials; Newton’s method; Gauss quadrature; Volterra; Fredholm | ||||
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