An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation

We report a new unconditionally stable implicit alternating direction implicit (ADI) scheme of O ( k 2 + h 2 ) for the difference solution of linear hyperbolic equation u tt + 2α u t + β 2 u = u xx + u yy + f ( x, y, t ), αβ ≥ 0, 0 < x, y < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where α > 0 and β ≥ 0 are real numbers. The resulting system of algebraic equations is solved by split method. Numerical results are provided to demonstrate the efficiency and accuracy of the method.