We consider the reaction-diffusion equation with discontinues coefficients and singular sources in one dimension. In this work, we construct ε-uniformly convergent High Order Compact (HOC) monotone… (More)

We propose a two-grid algorithm for implementation of a generalized A.M.Il’in’s scheme to a system of semilinear diffusion convection-dominated equations. To solve the nonlinear algebraic system of… (More)

A coupled system, where one is a degenerate parabolic equation and the other has no diffusion term, arises in the modeling of European options with liquidity shocks. Two implicit–explicit (IMEX)… (More)