Approximations for higher order boundary value problems using non-polynomial quadratic spline based on off-step points

摘要

Non-polynomial quadratic spline method based on off-step points is used to develop a numerical algorithm for obtaining an approximate solution of higher even order boundary value problems. For the employment of the method, decomposition procedure is used. Higher order boundary value problems are reduced into the corresponding system of second order boundary value problems. Convergence analysis of the method is also discussed. Seven numerical examples are given to illustrate the applicability and efficiency of new method. It is also shown that the new method gives approximations, which are better than those produced by other existing fourth order methods except higher degree splines.