Numerical solution of a quasilinear parabolic equation with a boundary layer
I. P. Boglaev
To solve a quasilinear parabolic equation with small parameter multiplying the derivatives with respect to the spatial variables, a numerical method is constructed with an estimate of the error, which is uniform with respect to the parameter. The construction of a nonlinear difference scheme is based on the method of straight lines and on the application of exact systems to one-dimensional problems. The computational mesh is chosen so that its density increases in a suitable way in the neighbourhood of the boundary. We propose that the nonlinear scheme be solved by an iterative algorithm, which converges uniformly with respect to the small parameter.
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USSR Computational Mathematics and Mathematical Physics, 1990, 30:3, 55–63
MSC: Primary 65M20; Secondary 65M50, 65M06, 35R35, 35K55, 35B25
I. P. Boglaev, “Numerical solution of a quasilinear parabolic equation with a boundary layer”, Zh. Vychisl. Mat. Mat. Fiz., 30:5 (1990), 716–726; U.S.S.R. Comput. Math. Math. Phys., 30:3 (1990), 55–63
Citation in format AMSBIB
\paper Numerical solution of a~quasilinear parabolic equation with a~boundary layer
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour U.S.S.R. Comput. Math. Math. Phys.
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