A powerful numerical technique for treating twelfth-order boundary value problems

Abstract

Abstract In this article, a fast algorithm is developed for the numerical solution of twelfth-order boundary value problems (BVPs). The Haar technique is applied to both linear and nonlinear BVPs. In Haar technique, the twelfth-order derivative in BVP is approximated using Haar functions, and the process of integration is used to obtain the expression of lower-order derivatives and approximate solution for the unknown function. Three linear and two nonlinear examples are taken from literature for checking the convergence of the proposed technique. A comparison of the results obtained by the present technique with results obtained by other techniques reveals that the present method is more effective and efficient. The maximum absolute and root mean square errors are compared with the exact solution at different collocation and Gauss points. The convergence rate using different numbers of collocation points is also calculated, which is approximately equal to 2.