Monotone difference schemes for equations with mixed derivatives

There are considered elliptic and parabolic equations of arbitrary dimension with alternating coefficients at mixed derivatives. For such equations, monotone difference schemes of the second order of local approximation are constructed. Schemes suggested satisfy the principle of maximum. A priori es...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2002-08, Vol.44 (3), p.501-510
Main Authors: Samarskii, A.A., Matus, P.P., Mazhukin, V.I., Mozolevski, I.E.
Format: Article
Language:English
Subjects:
Elliptic equations
Maximum principle
Mixed derivatives
Monotone difference scheme
Stability
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Summary:There are considered elliptic and parabolic equations of arbitrary dimension with alternating coefficients at mixed derivatives. For such equations, monotone difference schemes of the second order of local approximation are constructed. Schemes suggested satisfy the principle of maximum. A priori estimates of stability in the norm C without limitation on the grid steps τ and hα, α = 1,2,…, p are obtained (unconditional stability).
ISSN:0898-1221
1873-7668
DOI:10.1016/S0898-1221(02)00164-5