Efficient Hybrid Block Method For The Numerical Solution Of Second-order Partial Differential Problems via the Method of Lines

Olumide O. Olaiya; Rasaq A. Azeez; Mark I. Modebei

doi:10.46481/jnsps.2021.140

Authors

Olumide O. Olaiya
[email protected]
Department of Mathematics Programme, National Mathematical Centre, Abuja, Nigeria
Rasaq A. Azeez Department of Mathematics, University of Abuja, Abuja, Nigeria
Mark I. Modebei Department of Mathematics Programme, National Mathematical Centre, Abuja, Nigeria

Keywords:

Initial Value Problem, Boundary Value Problem, Block method, Linear Multistep Method, Hybrid method, mehod od lines

Abstract

This study is therefore aimed at developing classes of efficient numerical integration schemes, for direct solution of second-order Partial Differential Equations (PDEs) with the aid of the method of lines. The power series polynomials were used as basis functions for trial solutions in the derivation of the proposed schemes via collocation and interpolation techniques at some appropriately chosen grid and off-grid points the derived
schemes are consistent, zero-stable and convergent. the proposed methods perform better in terms of accuracy than some existing methods in the literature.

Dimensions

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