LAUSR

This work presents a numerical algorithm based on the cubic B-spline quasi-interpolation method for the simulation of one and two-dimensional hyperbolic partial differential equations. In this method, cubic B-spline quasi-interpolation method is used for the approximation of spatial derivatives which produces a system of second-order ordinary differential equations. Further, the obtained system is decoupled into a system of first-order ordinary differential equations, and then forward difference approximation for time derivative is used to get final solutions. Some well-known problems from the literature are considered to check the accuracy and efficiency of the proposed method.