Numerical solution of predator-prey models by the multistage differential transform method

Abstract

In this work, we present an dynamic behavior of the predator-prey models by using efficient computational algorithm, namely the multistage differential transform method(MDTM). The standard DTM is based on the Taylor series, but it differs from the conventional Taylor series in calculating coefficients. Because of nonlinearity as wall as large size of domain, it is difficult to obtain accurate numerical approximation for many problems by the standard DTM. To overcome these difficulties, we introduce an auxiliary function to apply the DTM for solving nonlinear problems and employ domain refinement to increase accuracy of approximate solution. Several illustrated examples of Holling types predator-prey models are demonstrated and numerical results are compared with those obtained by other numerical methods such as finite-difference and RK4.