Wavelet approach incorporated with optimization for solving stiff systems

Abstract

Wavelet-based methods open a door for numerical solution of differential equations. Stiff systems, a special type of differential equation systems, have the solutions with the components that exhibit complex dynamic behaviours such as singularities and abrupt transitions, which are hard to be captured by the typical numerical method or incur the computing complexity. This paper proposed to use the Wavelet-Galerkin scheme for solving stiff systems. Daubechies wavelet based connection coefficients, required in the Wavelet-Galerkin scheme, were computed using an algorithm that we recently rectified. The Lagrange multiplier method was incorporated into the wavelet approach in order to optimise the fitting of the initial conditions. Comparative studies were also carried out between the proposed approach and the Haar wavelet approach.