On a domain decomposition algorithm for a singularly perturbed reaction-diffusion problem

DOI10.1016/S0377-0427(98)00127-7zbMath0935.65103MaRDI QIDQ1301693

Igor P. Boglaev

Publication date: 12 September 1999

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergenceiterative algorithmnumerical resultssingular perturbationparallel computingfinite differencedomain decomposition methodreaction-diffusion problemtime discretization

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Parallel numerical computation (65Y05) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

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Cites Work

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• Finite difference domain decomposition algorithms for a parabolic problem with boundary layers
• Iterative algorithms of domain decomposition for the solution of a quasilinear elliptic problem
• Iterative domain decomposition algorithms for the solution of singularly perturbed parabolic problems
• Numerical solution of a quasilinear parabolic equation with a boundary layer
• A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation
• A note on the conditioning of upwind schemes on Shishkin meshes