Recursive Form of B-spline Based Collocation Solution to Homogeneous Differential Equations with Neumann's Boundary Value Problems

Abstract

The area of differential equations is a very broad field of study. The versatility of differential equations allows the area to be applied to a variety of topics from physics to population growth to the stock market. They are a useful tool for modeling and studying naturally occurring phenomena such as determining when beams may break as well as predicting future outcomes such as the spread of disease or the changes in populations of different species over time. Anytime an unknown phenomenon is changing with respect to time or space, a differential equation is involved Such differential equations have been solved by using many numerical methods. One numerical method which is developed by using simplified form of Recursive B-spline function in collocation method as basis function. The present method is used to solve second order and third order homogeneous differential equations with Neumann's boundary conditions. Solutions of Numerical examples for non -uniform length of the points show the efficiency of the method and easiness. Stability of B-spline based collocation method and accuracy of numerical solution is constantly improved by decreasing the nodal space.