NEWLY DEVELOPED SINGLE-STEP BLOCK METHOD FOR NUMERICAL SOLUTION OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

NEWLY DEVELOPED SINGLE-STEP BLOCK METHOD FOR NUMERICAL SOLUTION OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

A. F. Adebiyi, A. M. Udoye, L. S. Akinola, D. A. Matthew

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Abstract

This paper focuses on the development of a new block method for solving fourth order initial value problems of ordinary differential equations. Applying Chebyshev polynomial as a basis function, the method was developed using interpolation and collocation approaches. The convergence property of the method was established with zero-stability and consistency. Comparison was made with existing method, and the newly developed method compares favourably well.

Keywords

Numerical solution, Chebyshev polynomial, Error analysis, Zero stability, Convergence