Abstract
In the paper elliptic equations with alternating‐sign coefficients at mixed derivatives are considered. For such equations new difference schemes of the second order of approximation are developed. The proposed schemes are conservative and monotone. The constructed algorithms satisfy the grid maximum principle not only for coefficients of constant signs but also for alternating‐sign coefficients at mixed derivatives. The a prioriestimates of stability and convergence in the grid norm C are obtained.
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