Boundary Value Method for Direct Solution of Sixth-Order Boundary Value Problems

Abstract

In this work, 7th order continuous block methods called the Boundary Value Method (BVM) for the numerical approximation of sixth-order boundary Value Problem (BVPs) is proposed. These methods are derived using the Chebyshev polynomial as basis functions. The BVM comprises the main methods and additional methods, put together to form a block method and thus solved simultaneously to obtain an approximate solution for sixth-order BVPs. This method do not require a starting value as it is self-starting. The BVM is found to be consistent and its convergence was discussed. Numerical examples are shown to illustrate the applicability of the method. To show the efficiency of this method, the approximated solution derived from the methods is compared to the exact solutions of the problem and thus maximum errors are recorded and compared to those in other method from literature.