Wavelet-based collocation method for stiff systems in process engineering

Abstract

Abrupt phenomena in modelling real-world systems such as chemical processes indicate the importance of investigating stiff systems. However, it is difficult to get the solution of a stiff system analytically or numerically. Two such types of stiff systems describing chemical reactions were modelled in this paper. A numerical method was proposed for solving these stiff systems, which have general nonlinear terms such as exponential function. The technique of dealing with the nonlinearity was based on the Wavelet-Collocation method, which converts differential equations into a set of algebraic
equations. Accurate and convergent numerical solutions to the stiff systems were
obtained. We also compared the new results to those obtained by the Euler method and 4th order Runge-Kutta method.