Analysis Of Cubic Spline Method, B-Spline Method And Finite Difference Method For Solving Boundary Value Problems

Abstract

The thesis deals with analysis of cubic spline and cubic B-spline interpolation and nite di erence for boundary value problems. Investigation on the major problem specially on the behavior of the solutions and how to solve the ordinary di erential equations using cubic spline method, cubic B- spline interpolation and nite di erence methods. Cubic B-spline functions play important roles in both mathematics and engineering. To describe a numerical method for solving the boundary value problem with second-order using cubic B-spline, rst, the cubic B-spline basis functions are introduced, then we use the linear combination of cubic B-spline basis to approximate the solution. Finally, we obtain the numerical solution by solving tri-diagonal equations. The nite di erence method needs discretization with equal mesh sizes and replacing the BVP by di erence equations,which also involves tri-diagonal systems for the solution. Convergence and stability of the meth- ods will be discussed.The absolute errors in test examples are estimated , the comparison of approximate values and exact values and absolute error at the nodal point are shown tabularly and graphically . Further, shown that cubic B-spline method produces accurate result comparing with cubic spline and nite di erence methods.