Abstract
We consider the initial-boundary value problem for quasilinear parabolic equation with mixed derivatives and an unbounded nonlinearity. We construct unconditionally monotone and conservative finite-difference schemes of the second-order accuracy for arbitrary sign alternating coefficients of the equation. For the finite-difference solution, we obtain a two-sided estimate completely consistent with similar estimates for the solution of the differential problem, and also obtain an important a priori estimate in the uniform C-norm. These estimates are used to prove the convergence of finite-difference schemes in the grid L2-norm. All theoretical results are obtained under the assumption that some conditions imposed only on the input data of the differential problem are satisfied.
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Matus, P.P., Hieu, L.M. & Pylak, D. Monotone Finite-Difference Schemes of Second-Order Accuracy for Quasilinear Parabolic Equations with Mixed Derivatives. Diff Equat 55, 424–436 (2019). https://doi.org/10.1134/S0012266119030157
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DOI: https://doi.org/10.1134/S0012266119030157