1. A spectral collocation method for solving Caputo-Liouville fractional order Fredholm integro-differential equations.
- Author
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Saad, Khaled M. and Khirallah, M. Q.
- Subjects
- *
FREDHOLM equations , *INTEGRO-differential equations , *ALGEBRAIC equations , *NEWTON-Raphson method , *COLLOCATION methods , *INTEGER approximations , *NUMERICAL integration - Abstract
In this paper, a numerical method for solving the fractional order Fredholm integrodifferential equations via the Caputo-Liouville derivative is presented. The method uses the wellknown shifted Chebyshev expansion and a truncated series to represent the unknown function. It also incorporates numerical integration techniques like the Trapezoidal, Simpson's 1/3, and Simpson's 8/3 methods. The paper also provides an approximation for the derivative of an integer. The procedure converts the provided problem into a system of algebraic equations using shifted Chebyshev coefficients and collocation points. The coefficients are found by solving this system using well-known techniques like Newton's method. Numerical results are presented graphycally to illustrate the applicability, efficacy, and accuracy of the approach presented in this work. All calculations in this study were performed using the MATHEMATICA software program. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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