The second‐order central difference is often used to approximate the derivatives of the wave equation. It is demonstrated that gains in computational efficiency can be made by using high‐order approximations for these derivatives. A one‐dimensional model is used to illustrate the relative accuracy of [Formula: see text] central‐difference schemes. For comparison, [Formula: see text] pseudospectral schemes are used as an additional measure of performance. The results indicate that [Formula: see text] differencing can achieve similar accuracy as the [Formula: see text] spectral scheme. For practical illustration, a two‐dimensional form of the [Formula: see text] algorithm is used to compute the exploding reflector response of a salt‐dome model and compared with a fine‐grid [Formula: see text] result. Transmissive sponge‐like boundary conditions are also examined and shown to be effective.

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