Solving System of Ordinary Differential Equation Using SAWI Transformation

Abstract

The study examines the use of Shifted and Weighted Integral (SAWI) transformation in the solution of systems of ordinary differential equations (ODEs). SAWI is a comparatively new integral transform that is based on Fourier integrals and it is characterized by its ability to translate a given differential equation into algebraic forms thus making the process of finding a solution a lot simpler and yet, preserving the accuracy of the solution. This paper uses the SAWI transformation method to dynamics of linear first-order and second-order ODEs with constant coefficients. This technique is proved to be efficient by its comparison with the precise solutions acquired by MATLAB. Numerical solutions of two representative problems such as a chemical kinetics model and a second-order system coupled system, the SAWI transformation yields a solution that is identical to the analytical solutions of the test problems involved. The results also propose the potential of SAWI as an effective, accurate and computationally feasible alternative to conventional numerical approaches to the solution of ODE systems with broad implications to applied mathematics, engineering, and scientific modelling.