Abstract

ONE STEP HYBRID BLOCK METHOD FOR THE SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Yunusa, S.,1 Mohammed, G.A.,1 Etuk, E.D.,1 Aliyu, Y.A.1 and Garba, U.2

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In this paper, a new k-step hybrid block method was derived for the solution of first order initial value problems (IVP) of ordinary differential equations (ODEs). A continuous linear multistep method (CLMM) with variable coefficients was developed using interpolation and collocation of a polynomial approximate solution. This CLMM was evaluated at some selected off-grids points which give a class of discrete linear multistep methods (DLMMs) and was implemented as a block method. Investigations on the properties of the method such as, order, zero-stability, consistency were carried out and the results indicated that the method were of order three, A-stable and convergent. MATLAB codes were written to test the numerical performance of the block method on some linear and non-stiff IVPs of ODEs and the results showed that the one step hybrid block method (HBM) compared favorably with the existing method. Keywords: One step, interpolation, collocation, hybrid and block method.

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