Construction Of Difference Schemes For Nonlinear Singular Perturbed Equations By Approximation Of Coefficients. (arXiv:1002.2925v1 [math.NA])

Construction Of Difference Schemes For Nonlinear Singular Perturbed Equations By Approximation Of Coefficients. (arXiv:1002.2925v1 [math.NA]): "

Mathematical modeling of many physical processes such as diffusion, viscosity
of fluids and combustion involves differential equations with small
coefficients of higher derivatives. These may be small diffusion coefficients
for modeling the spreading of impurities, small coefficients of viscosity in
fluid flow simulation etc. The difficulty with solving such problem is that if
you set the small parameter at higher derivatives to zero, the solution of the
degenerate problem doesn't correctly approximate the original problem, even if
the small parameter approaches zero; the solution of the original problem
exhibits the emergency of a boundary layer. As a result, the application of
classical difference schemes for solving such equations produces great
inaccuracies. Therefore, numerical solution of differential equations with
small coefficients at higher derivatives demands special difference schemes
exhibiting uniform convergence with respect to the small parameters involved.
In this article author investigates two nonlinear boundary value problems on a
finite interval, resulting in exponential and power-law boundary layers.

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