On a finite difference analogue of a singular boundary value problem.
On a finite difference analogue of forth order for boundary value problem.
On a fourth-order finite difference method for nonlinear two-point boundary value problems.
On collocation methods for singular perturbation problems of convection-diffusion type.
On difference schemes for quasilinear evolution problems.
On numerical solution of a mildly nonlinear turning point problem
On simulations of the classical harmonic oscillator equation by difference equations.
On the numerical solution of the diffusion equation with a nonlocal boundary condition.
On the Structure of Error Estimates for Finite-Difference Methods.
Opposing flows in a one dimensional convection-diffusion problem
In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...