NUMERICAL APPROXIMATION OF MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATION BY GALERKIN METHOD WITH CHEBYSHEV POLYNOMIAL BASIS

Document Type : Regular research papers

Authors

1 Department of Applied Sciences, Federal College of Dental Technology and Therapy, Enugu, Nigeria

2 Department of Mathematics, University of Ilorin, Ilorin, Nigeria.

3 Department of Mathematics, University of Ilorin

4 Department of Mathematics, University of Abuja, Abuja, Nigeria.

Abstract

The Galerkin method is a numerical technique used to approximate solutions to Partial Differential Equations (PDEs) or integral equations. To this end, this study employed the Galerkin method to address Multi-Order Fractional Differential Equations (MFDEs), utilizing Chebyshev Polynomials as the basis functions. The approach involved assuming an approximate solution using shifted Chebyshev polynomials, which was then substituted into the given problem. Subsequently, boundary conditions were applied. The residual equation, integrated over the interval of interest along with the weight function, resulted in a linear system of equations with unknown Chebyshev coefficient constants. Maple 18 was utilized to determine these unknown constants, which were then substituted back into the assumed solution to obtain the desired approximate solution. To assess the effectiveness of the proposed technique, numerical examples were solved, and the results were compared with existing literature. The comparison showcased that the suggested algorithm is not only accurate but also efficient in multi-order fractional differential equations. Tables and figures were employed to present and illustrate the obtained results.

Keywords

Main Subjects

Files

Share

How to cite

Statistics