Non-polynomial cubic triplet parameter spline scheme for second-order boundary value problem systems

Understanding second-order boundary value problems (BVPs) aids in modelling and predicting various real-world phenomena, crucial for scientific and engineering advancements. This study proposes the development of an effective numerical method based on cubic splines and non-polynomial triplet parameters for approximations to the solution of systems of second-order BVPs. This method extends the non-polynomial cubic spline's trigonometric part by three additional parameters, which makes it superior to other existing numerical techniques. The cherry on top is the suggested scheme's adaptability to different step sizes. With the inclusion of CPU time, this analysis gets more fascinating. Comparatively speaking to alternative spline, collocation, and finite difference approaches, the current algorithm provides better approximations. To build a solid foundation for the suggested method, the convergence analysis of the proposed algorithm is discussed. Numerical examples are used to demonstrate the suggested method's utility in practice.