DEVELOPMENT OF BLOCK HYBRID BACKWARD DIFFERENTIATION FORMULAE FOR SOLVING SOME CLASSES OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

The need for numerical solutions of second order ordinary differential equations cannot be over emphasized, as mathematical problems of it kind results from numerous filed such as science, engineering among others. In this research, we focus on the derivation of a k-step Block Hybrid Backward Differentiation Formulae of order (k+1) for the general solution of second order ordinary differential equations. The new methods were derived using the procedure of collocation and interpolation of power series at some selected grid and off-grid points. The methods were used to compute the solution of linear and nonlinear systems in a block by some discrete schemes obtained from the continuous schemes which are combined and implemented. The methods were tested on some classes of second order ordinary differential equations, the results indicated that all the methods has a maximum error of and as step number increases methods give more accurate results with small errors.