We study an initial-boundary value problem for a singularly perturbed reaction–convection–diffusion system. Asymptotic analysis is used to construct a domain decomposition method for the system to describe the asymptotic nature of the interactions between the boundary layers, interior layers and shock layers. Our results show that the formation of boundary layers and shock layers depends upon i...

in this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. a numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. truncation errors are derived for both continuous and discontinuous problems. parameter uni...

In the stably stratified interior of the ocean, mesoscale eddies transport materials by quasiadiabatic isopycnal stirring. Resolving or parameterizing these effects is important for modeling the oceanic general circulation and climate. Near the bottom and near the surface, however, microscale boundary-layer turbulence overcomes the adiabatic, isopycnal constraints for the mesoscale transport. I...

A singularly perturbed time-dependent convection-diffusion problem is examined on non-rectangular domains. The nature of the boundary and interior layers that arise depends on the geometry of the domains. For problems with different types of layers, various numerical methods are constructed to resolve the layers in the solutions and the numerical solutions are shown to converge independently of...

In recent years, the Indian Ocean (IO) has been discovered to have a much larger impact on climate variability than previously thought. This paper reviews processes in which the IO is, or appears to be, actively involved. We begin the mathematical model with a pattern for summer monsoon winds. Three dimensional temperature and velocity fields are calculated analytically for the ocean forced by ...

Semilinear reaction-diffusion two-point boundary value problems with multiple solutions are considered. Here the second-order derivative is multiplied by a small positive parameter and consequently these solutions can have boundary or interior layers. A survey is given of the results obtained in our recent investigations into the numerical solution of these problems on layer-adapted meshes.