Abstract
The present paper is devoted to constructing second-order monotone difference schemes for two-dimensional quasi-linear parabolic equation with mixed derivatives. Two-sided estimates of the solution of specific difference schemes for the original problem are obtained, which are fully consistent with similar estimates of the solution of the differential problem, and the a priori estimate in the uniform norm of C is proved. The estimates obtained are used to prove the convergence of difference schemes in the grid norm of L2.
Highlights
Проблемы разработки разностных схем для уравнений со смешанными производными были изучены в [4,5,6]
The present paper is devoted to constructing second-order monotone difference schemes for two-dimensional quasi-linear parabolic equation with mixed derivatives
Two-sided estimates of the solution of specific difference schemes for the original problem are obtained, which are fully consistent with similar estimates of the solution of the differential problem, and the a priori estimate in the uniform norm of C is proved
Summary
Проблемы разработки разностных схем для уравнений со смешанными производными были изучены в [4,5,6]. Difference schemes for quasilinear parabolic equations with mixed derivatives. В теории разностных схем [1; 2] принцип максимума применяется для исследования устойчивости и сходимости разностного решения в равномерной норме. В [7] для эллиптических уравнений со смешанными производными используются новые монотонные и консервативные разностные схемы как для знакопостоянного, так и для знакопеременного коэффициентов.
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