IMPLICIT HYBRID BLOCK METHODS FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEMS OF THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

Algorithms of direct solution of initial value problems of special and general third order differential equations were developed in this thesis. The hybrid methods were derived based on the approach of collocation of the differential system obtained from the basis function and the interpolation of the approximate solution at the grid off points. The hybrid method has the advantage of easy change of step size and evaluating functions at off-step points, producing self starting schemes without developing predictors separately. The block method approach was adopted for its implementation. The basic properties of the methods were analyzed using appropriate techniques and were found to be consistent, zero- stable, convergent, and Stable. The methods were coded using Mat – lab codes such that it is easy to run without learning special programming language or package. The performance of the methods were tested by using them to solve some sample initial value problems of special and general third order ordinary differential equations and were found to compare favorably with existing methods developed by some prominent researchers.