An Improved L-Stable Scheme for Initial Value Problems Under Variable Step-Size Approach

Abstract

A non-linear explicit scheme has been studied for autonomous and non-autonomous initial value problems in ordinary differential equations (ODEs). This research proposed fifth order of convergence. The stability region of the scheme is also shown, as is the evolution of the scheme's associated local truncation error. A few numerical experiments showed that the scheme is fit for initial value problems with singular solutions, blowup the ODEs, singularly perturbed and stiff problems. MATLAB R2019a was used for the numerical computations and plotting of results produced by all methods.

Keywords. Nonlinear method, local truncation error, L-Stability, Variable step-size, autonomous and non-autonomous.