Abstract

APPLICATION OF THE SHIFTED LEGENDRE POLYNOMIALS OF THREE STEP HYBRID BLOCK METHOD FOR THE SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Yunusa, S.,1 Mohammed, G.A.,2 Pantuvo. T. P.3 and Etuk, E. D.4

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In this paper, we discussed the application of the shifted Legendre polynomials as approximate solution of three step hybrid block method for the solution of first order initial value problems of ordinary differential equations. The continuous formulation for the method was obtained by interpolation and collocation which was evaluated at some selected grid points to generate the discrete block method. The order, consistency, zero stability, convergent and stability region for the method were examined. The method was then applied in block form as simultaneous numerical integrators over non-overlapping intervals. The results from the new method compared with those obtained from existing methods revealed that the new method gives better accuracy. Keywords: Three step, Legendre polynomials, interpolation, collocation, hybrid and block method.

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