SERIES AND EXPONENTIALLY-FITTED TWO-POINT HYBRID METHODS FOR GENERAL SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this work, the numerical solution of initial value problems of second order ordinary differential equations have been studied. A class of continuous implicit hybrid algorithms for the solution of initial value problems of general second order ordinary differential equations has been developed using a combination of power series and exponential functions as basis function. The interpolation and collocation techniques on the basis function and its differential system at grid and off grid points respectively were adopted to generate a class of two-point hybrid methods. The class of two-point hybrid methods are found to be consistent, symmetric and zero stable. Predictor-corrector mode was used for the implementation of the main schemes. To avoid the major set-back of predictor-corrector approach, consistent, symmetric and zero stable predictors of the same order with the main schemes were developed for the implementation of the implicit schemes. Accuracy of the methods is confirmed with sample problems solved with MATLAB software. Absolute errors obtained were compared with those of a few existing methods.