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Solving Fisher's Equation using Modified Exponential Cubic B-Spline Differential Quadrature

Mostafa M. A. Atallah *, Rabab M. I. El-Hassani **, Ramy F. Taki El Din ***

*-*** Faculty of Engineering, Ain Shams University, Cairo, Egypt.

Periodicity:July - December'2020
DOI : https://doi.org/10.26634/jmat.9.2.17941

Abstract

In this paper, we aim to compare traditional numerical techniques used for solving the well known nonlinear Fisher's equation with our proposed technique, Differential Quadrature (DQ) method with a Modified Exponential Cubic B-Spline as a base function. In principle, the proposed DQ method used the modified exponential cubic B-spline as a test function to deduce some coefficients that convert the given partial differential equation to a system of ordinary differential equations. The latter system is solved numerically using a 4^th order Runge-Kutta (RK) method. In our study, the comparison is considered on two different forms of Fisher's partial differential equation u_t = λu_xx + φ(u). Comparisons to traditional techniques are carried out using three different error types. The superiority of the proposed DQ method over commonly used traditional numerical methods has been recorded. Numerical results showed that the Modified Exponential Cubic B-Spline DQ method yields acceptable and mostly accurate solutions.

Keywords

Differential Quadrature, Modified Exponential Cubic B-Spline, Fisher's Equation, Numerical Methods, Partial Differential Equations.

How to Cite this Article?

Atallah, M. M. A., El-Hassani, R. M. I., and Din, R. F. T. E. (2020). Solving Fisher's Equation using Modified Exponential Cubic B-Spline Differential Quadrature. i-manager's Journal on Mathematics, 9(2), 8-17. https://doi.org/10.26634/jmat.9.2.17941

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