The decomposition method for singularly perturbed boundary value problems with the local perturbation of the initial conditions. Equations with convective terms
The Dirichlet problem for singularly perturbed parabolic equations in one space variable is considered. The initial condition has unit local perturbations of a finite amplitude on a narrow subdomain of width \(2\delta\) and the perturbation parameter \(\varepsilon^2\) is the coefficient of the highest derivative occurring. It is shown that there does not exist rectangular piecewise uniform grids for classical difference schemes, so that the schemes would converge uniformly in \(\delta\) and \(\varepsilon\). However, using the method of additive selective of singularities and mobile concentrating grids monotone finite difference schemes can be constructed.
scientific article; zbMATH DE number 1175138