Abstract
We derive a new finite difference scheme which is easily extended to fourth-order accurate in both temporal and spatial dimensions. It is shown through a discrete Fourier analysis that the method is unconditionally stable for a 2D problem. It requires only a regular seven-point difference stencil similar to that used in the standard second-order algorithms, such as the Crank–Nicolson algorithm. Numerical experiments are conducted to test its high accuracy and efficiency of the new algorithm.
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