HYBRID LINEAR HALF-STEP METHODS FOR DIRECT SOLUTION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

Hybrid numerical methods for solving direct solution of initial value problems of general second order differential equations have been studied in this dissertation. Using power series as the basis function, the collocation and interpolation approach is adopted to develop continuous implicit hybrid half step methods which are evaluated at both grid points and off-grid points to generate discrete methods. Block method is used to solve the discrete schemes derived and basic analyses which include zero-stability, order, error constant and region of absolute stability are verified. Examples are tested using efficient computer codes and the results are compared with existing methods which was found to be better.