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11. HYBRID LINEAR MULTISTEP STO ̈RMER-COWELL TYPE METHODS FOR THE SOLUTION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS by Olabode B. T. and Senewo E. O. Volume 50 (March, 2019 Issue)
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HYBRID LINEAR MULTISTEP STO ̈RMER-COWELL TYPE METHODS FOR THE SOLUTION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Olabode B. T. and Senewo E. O.

Department of Mathematical Sciences, Federal University of Technology Akure, Ondo State.

Abstract

A class of hybrid linear multistep Sto ̈rmer-Cowell type methods for solution of second order initial value problems (IVPs) of ordinary differential equations (ODEs) without reducing it to an equivalent system are introduced. This paper adopted power series as its basis function. The approach of interpolation of the approximate solution and collocation of the derivative systems at some selected grid and off grid points was employed. The two schemes with step numbers k = 2 and k = 3 were developed and analysed based on order, error constant, zero stability, consistence and convergence. The derived schemes were implemented in block mode and the results compared with those of existing methods.

Keywords: Sto ̈rmer-Cowell, interpolation, collocation, Approximate solution, Grid- point, Continuous method

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