Block Nystrom type method and its block extension for fourth order initial and boundary value problems

Abstract

The derivation of Block Nyström type Method (BNTM) which is not normally used as numerical integrator of boundary value problems 184 E.O. Adeyefa et al. (BVPs) is considered and directly applied to solve both initial value problems (IVPs) and BVPs in ordinary differential equations (ODEs). Collocation technique is adopted in the derivation of the BNTM which is applied as simultaneous integrator to fourth order ODEs. The BNTM possesses the desirable feature of being self-starting as the implementation is in block form. The paper concludes by solving Numerical examples which establish the effectiveness and accuracy of the method. The superiority of BNTM is established by the numerical values presented.

A new class of orthogonal polynomials as trial function for the derivation of numerical integrators

“…The numerical solution of ODEs by collocation methods has been studied (see [1], [2], [3], [4], [5], [6], [7]). In the recent years, the solutions of (1) for cases m = 1, 2 & 3 have been extremely discussed (see [8], [9], [10], [11], [12]). The approach of reducing the higher order of (1) to a system of first order and the consequent setback has also been discussed in [13].…”

“…Solving(9) and(10) and substituting the outcomes into (8), we have) 11 ( .... .......... .......... .......…”