Abstract: We propose a class of high-order compact finite
difference schemes for solving two-dimensional parabolic problems with a mixed
derivative. The schemes are fourth-order accurate in space and second- or
lower-order accurate in time depending on the choice of a weighted average
parameter m.
Unconditional stability is proved for and numerical experiments
supporting our theoretical analysis and confirming the high-order accuracy of
the schemes are provided.
Keywords and phrases: parabolic problems, mixed derivative, compact scheme, stability.
