An algorithm for solving initial value problems of third order ordinary differential equations

Abstract

We propose an implicit multi-step method for the solution of initial value problems (IVPs) of third order ordinary differential equations (ODE) which does not require reducing the ODE to first order before solving. The development of the method is based on collocation of the differential system and interpolation of the approximate solution at selected grid points. This generates a system of equations, which are then solved using Gaussian elimination method. Three predictors, each of order 5, are also proposed to calculate some starting values in the main method. Analysis of basic properties is considered to guarantee the accuracy of the method. The results for method of step length k = 5 when compared with that of step length k = 4 show a better level of accuracy.

KEYWORD: Zero stable, third order IVPs, predictor method, step length.