Algorithmic collocation approach for direct solution of fourth-order initial-value problems of ordinary differential equations

An Order Six Zero-Stable Method for Direct Solution of Fourth Order Ordinary Differential Equations

“…The accuracy of the method (14) was tested with two test problems and their results compared with existing method [6] as shown in the tables below. Test Problem 1: [6] and New Method (14) for Problem 1…”

“…The approach of reducing such equations to a system of first order equations leads to serious computational burden and wastage in computer time [2], [3] . Many attempts have been made to formulate numerical algorithms capable of solving special problem of type (1) without reducing it to system of first order equations [7], [9], [11], [12] .…”

“…Many attempts have been made to formulate numerical algorithms capable of solving special problem of type (1) without reducing it to system of first order equations [7], [9], [11], [12] . Multiderivative methods for direct solution of problem (1), taking m = 4, have been considered using canonical polynomial as the basis functions [4], [5] . They produced methods with many function evaluations.…”

“…Efforts are made to develop a zero-stable order six method of higher step-number with reduced functions evaluation for direct solution of problem (1) for m = 4. The reduced functions evaluation of this method further lessened the computational burden [3], [6] .…”

“…Exact solution Computed Method (14) Awoyemi and Kayode [6] Error in Method (14) 0 [6] and New Method (14) for Problem 2 X Exact solution Computed Method (14) Awoyemi and Kayode [6] Error in Method ( Tables 1 and 2 above show the results of problems 1 and 2 respectively when solved with the new method (14). The maximum errors arising from the problems when solved with the existing methods [6] for a mesh size h=1/32 were compared with the errors of the new method (14) for the same mesh size as shown in the Tables.…”