HYBRID BACKWARD DIFFERENTIATION FORMULAS FOR THE SOLUTION OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This study focuses on formulation of hybrid backward differentiation methods with power series as basis function through interpolation and collocation approach for solving initial value problems of first order ordinary differential equations. The step numbers for the derived hybrid methods are k = 5 and 6. The schemes are analysed using appropriate theorems to investigate their consistency, stability, convergence and the investigation shows that the developed schemes are consistent, zero stable and hence convergent. The stability property of the methods was also investigated and findings reveal that the methods are A-stable which make them suitable for solving the class of problems considered in this project such as linear and non-linear problems, oscillatory problems and stiff system. The implementation results on these problems show that the methods are of higher accuracy and have superiority over some other existing methods considered in the literature.