An Unconditionally Stable Spline Difference Scheme for Solving the Second 2D Linear Hyperbolic Equation

In this paper, an unconditionally stable implicit difference scheme based on quartic spline interpolations in space direction and finite difference discretization in time direction for the numerical solution of two-dimensional linear hyperbolic equation is proposed. The proposed scheme is second-order accurate in time direction and fourth-order accurate in space direction. Numerical examples are tested to illustrate the efficiency of the new difference scheme.