Application of the Extended Cubic Bézier Interpolation Method to the Boundary Value Problems

In this study, linear second order differential equations with Dirichlet boundary conditions which are used in civil engineering, thermodynamics, electrostatics, fluid dynamics are considered and the extended cubic Bézier interpolation method is employed to approximate the solutions. The extended form contains three shape parameters which enable to get more accurate results without the necessity of increasing the degree of the curve. Based on the root mean square error, it is also observed that this method produce better approximations than cubic B-spline method.