Solution of stiff ordinary differential equations by Aboodh transform method

Abstract

The stiff differential equation occurs in almost every field of science. These systems are encountered in electric circuits, mathematical biology, chemical reaction process, meteorology, mechanics and vibrations. The use of normal numerical approaches to analyse and predict such systems requires more time and memory, and getting an exact solution is utterly uneconomical and unreliable. When dealing with a stiff system using numerical approaches, stability problem emerges. In getting over this restriction, the Aboodh transform is suggested as one of the convenient tools to obtain closed-form solutions for linear and nonlinear stiff ordinary differential equations due to it mathematical simplicity. In this paper, we considered some examples to demonstrate the simplicity and potency of the Aboodh transform method in providing an exact solution to the linear stiff ordinary differential equation and comparing the answer with the Laplace transform method.