An Adaptive Step-Size Taylor Series Based Method and Application to Nonlinear Biochemical Reaction Model

摘要

In this study, a Taylor series based method, which is the multi-step Differential Transform Method (DTM), is adapted to define a new adaptive step-size semi-analytical and numerical method. This new approach is applied to a nonlinear biochemical reaction model to obtain approximate analytical solutions in the form of piecewise convergent series with easily computable components. The numerical results obtained by using the present method are compared to those obtained by using the classical DTM, classical multi-step DTM and Runge-Kutta method. The present method gives a more accurate approximation with less computational effort than fixed step-size methods.