DEVELOPMENT OF FALKNER-TYPE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

DEVELOPMENT OF FALKNER-TYPE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

ABSTRACT

This research focuses on the formulation of block hybrid methods with power series as basic function through interpolation and collocation techniques for numerical solution of second order initial value problems in ordinary differential equations. The step number for the derived block hybrid method is k=2 with two off-step point and four offstep points. The basic properties of numerical methods were analyzed and findings revealed that the methods were consistent, zero-stable and convergent which makes them suitable for solving the class of problems considered such as linear and non-linear problems, oscillatory problems, Dynamic problem and Stiff system. The results obtained from the proposed methods, show that the methods are of higher accuracy and have superiority over some existing methods considered in the literature.

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