B-Spline Collocation Method for Solving Time-Dependent Differential Equations

Dr. Y. Rajashekhar Reddy

Abstract: This paper presents the use of B-spline collocation methods for solving time-dependent partial differential equations (PDEs) and ordinary differential equations (ODEs). B-splines, known for their flexibility and local support, are used as basic functions in a collocation framework. We validate the method on classical problems like the heat equation and second-order ODEs, showing high accuracy and efficiency.

Keywords: B-spline, collocation method, time-dependent PDE, numerical analysis, heat equation