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Difference schemes on irregular grids for equations of mathematical physics with variable coefficients. (English. Russian original) Zbl 1022.65092

Comput. Math. Math. Phys. 41, No. 3, 379-391 (2001); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 3, 407-419 (2001).
This paper is devoted to new difference schemes of second-order approximation on irregular grids with the use of conventional stencils for stationary and nonstationary problems. For multidimensional problems, efficient schemes of vector additive type are constructed. Numerical experiments carried out in this work indicate improved accuracy of new algorithms on coarse grids as compared to the known second-order accuracy schemes of the first approximation order.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations
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