Cubic B-Spline Technique for Numerical Solution of Second Order Convection-Diffusion PDEs

This paper introduces an innovative cubic B-spline method designed for computing precise numerical solutions to linear partial differential equations in one dimension. Through a comprehensive error analysis, the proposed technique has been extensively evaluated, showcasing its robust stability. Its application across diverse convection-diffusion linear problems-encompassing fields such as heat transfer, acoustics, and mass transfer-has proven its efficacy and accuracy. Comparative assessments against exact solutions have highlighted the superiority of our method, consistently delivering improved numerical outcomes.