Boundary value problems of second order ordinary differential equations: A cubic B-spline and finite difference method

An overview of the finite difference approach and basis spline of cubic form interpolation for solving ordinary differential equation boundary value issues is given in this work. To create a numerical technique for solving second-order two-point boundary value problems, it primarily concentrates on the basis spline of cubic form functions. We study cases of ordinary differential equations for homogeneous and non-homogeneous, zero and non-zero boundary conditions, with constant and variable coefficients. Applications of differential equations with conditions imposed at distinct sites, such as the two-point boundary value issue, can be found in engineering, mathematics, and other scientific fields. By resolving tri-diagonal systems, we eventually arrive at the numerical solution. Examples comparing the results with the finite difference approach and basis spline of cubic form demonstrate the practicality and efficiency of the cubic B-spline method. The absolute errors are calculated for test cases, and a visual comparison of approximate values, exact values, and absolute errors at the nodal points is provided.