A new unconditionally stable compact difference scheme of O(tau2+h4) for the 1D linear hyperbolic equation

Abstract In this paper, we propose a three level compact difference scheme of O ( τ 2 + h 4 ) for the difference solution of one-dimensional second-order non-homogeneous linear hyperbolic equation u tt + 2 α u t + β 2 u = u xx + f ( x , t ) , 0 x 1 , t > 0 , where α > β ⩾ 0 . Stability analysis of the method has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.

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