Abstract
This paper examines the derivation of hybrid numerical algorithms with step length(k) of five for solving fourth order initial value problems of ordinary differential equations directly. In developing the methods, interpolation and collocation techniques are considered. Approximated power series is used as interpolating polynomial and its fourth derivative as the collocating equation. These equations are solved using Gaussian-elimination approach in finding the unknown variables aj, j=0,...,10 which are substituted into basis function to give continuous implicit scheme. The discrete schemes and its derivatives that form the block are obtainedby evaluating continuous implicit scheme at non-interpolating points. The developed methods are of order seven and the results generated when the methods were applied to fourth order initial value problems compared favourably with existing methods.order initial value problems compared favourably with existing methods.
Highlights
This paper examines the derivation of hybrid numerical algorithms with step length(k) of five for solving fourth order initial value problems of ordinary differential equations directly
The general fourth order initial value problem of ordinary differential equations of the form mate numerical method for the first order would be used to solve the system. This approach is been attached with lots of setbacks which include: computational burden, lots of human effort, complexity in developing computer code which affects yiv = f (x, y(x), y (x), y (x), y (x)), y(x0) = y1, y (x0) = y2, y (x0) = y3 (1)
In the past, solving fourth order ordinary differential equations (ODEs) requires reducing tion method, the direct method of solving ODEs of higher order was developed by lots of scholars which include Akeremale et al [4], Abolarin et al [5], Kuboye et al [6], Omar & Kuboye
Summary
This paper examines the derivation of hybrid numerical algorithms with step length(k) of five for solving fourth order initial value problems of ordinary differential equations directly. The general fourth order initial value problem of ordinary differential equations of the form mate numerical method for the first order would be used to solve the system This approach is been attached with lots of setbacks which include: computational burden, lots of human effort, complexity in developing computer code which affects yiv = f (x, y(x), y (x), y (x), y (x)), y(x0) = y1, y (x0) = y2, y (x0) = y3 (1). Numerical methods for solving equation (1) were proposed by Omar and Kuboye[15], Areo and Omole[16] and Mohammed[17] These current methods solved directly equation (1) but its accuracy in terms of error can still be improved. This paper examines the derivation and implementation of the efficient numerical algorithm for solving fourth order ordinary differential equations directly and it focuses on improving the accuracy of the existing methods
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