New Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems

In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This is based on basis functions with for the second-order derivative. The theoretical derivative and error analysis have been successfully derived. We found that was O(h3) accurate. By using approximation, proposed O(h5) Four numerical consisting of ordinary differential equations trigonometric different step sizes were performed validate accuracy methods. results compared least squares method, finite difference element volume interpolation extended exact solutions. finding maximum errors, consistently showed gave best approximations among existing also our involved simple implementation straightforward computations. Hence, efficiency can say reliable promising solving BVPs.