Cubic Spline Interpolant for Approximating Solutions of Linear Differential Equations

Abstract

We have studied in this thesis a class of numerical methods for interpolating and solving linear differential equations. The method based on the temporal semi-discretization by implicit Euler finite difference method and a cubic spline discretization in the spatial direction on uniform mesh. We give some theorems of the existence and uniqeness of the spline functions. We also give some considerable properties for convergence. A systematic procedure for determining the formula for a natural cubic spline from a table of interpolating values are explained. We compared the exact and the approximate solutions for some examples using MATLAB.