On the Construction and Comparison of an Explicit Iterative Algorithm with Nonstandard Finite Difference Schemes

Abstract

An explicit iterative algorithm to solve both linear and nonlinear problems of ordinary differential equations with initial conditions is formulated with main focus given on its comparison with some non-standard finite difference schemes. Two first order linear initial value problems (IVPs) with periodic behavior are used to analyze the performance of the proposed algorithm with respect to maximum absolute error and computational effort where proposed algorithm performs better in both cases. The proposed algorithm efficiently follows the oscillatory behavior of models like Lotka-Volterra predator-prey and mass-spring system (damped case) in comparison to the nonstandard schemes. All necessary computations have been carried out through MATLAB version 8.1 (R2013a) in double precision arithmetic. Numerical results obtained by the proposed algorithm are found to be computationally reliable and practical in comparison with two nonstandard finite difference schemes discussed in literature.

Keywords: Iterative algorithm, nonstandard finite difference scheme, Initial conditions, Maximum absolute error.