Comparison of Stability of Selected Numerical Methods for Solving Stiff Semi-Linear Differential Equations
Kwaku Darkwah, Isaac Azure

Abstract
Attention was focused on the explicit Exponential Time Differencing (ETD) integrators that are designed to solve stiff semi-linear problems. Semi-linear PDEs can be split into a linear part, which contains the stiffest part of the dynamics of the problem, and a nonlinear part, which varies more slowly than the linear part. The ETD methods solve the linear part exactly, and then explicitly approximate the remaining part by polynomial approximations. The research involves an analytical examination and comparison of the asymptotic stability properties of some Exponential Time Differencing Schemes (ETD1, ETD2, ETD2RK1 and ETD2RK2) methods in order to present the advantage of these methods in overcoming the stability constraints.

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