Collocation Method for the Solution of Boundary Value Problems

Abstract

In mathematics, collocation method is a method for the numerical solution of ordinary differential, partial differential and integral equations. The idea is to choose a finite-dimensional space of candidate solutions (usually polynomial up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the given equation at the collocation points. A numerical method for solving non-linear two-point boundary value problems was implemented which based on collocation method. Two-point Taylor polynomial of order six was used as trial function to obtain the residual function. The method was implemented on some existing problems solved with other numerical methods to show that the method can be equal used to solve the problem, the results obtained were compared to verify the reliability and accuracy of the method and it was observed that collocation method is more effective in each case because the error is minimal compare with the results obtained with the other numerical methods.