where λ and m are arbitrary constants and C(U) is an arbitrary smooth function, has been done. The symmetries obtained for constructing exact solutions of the relevant equations have been successfully applied. In the particular case, new exact solutions of nonlinear reactiondiffusion-convection (RDC) equations arising in applications have been found. The most general RDC equation with power fun...

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two–phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimizat...

We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been cond...

This chapter presents a constructive derivation of HDG methods for convection-diffusion-reaction equation using the Rankine-Hugoniot condition. This is possible due to the fact that, in the first order form, convection-diffusion-reaction equation is a hyperbolic system. As such it can be discretized using the standard upwind DG method. The key is to realize that the Rankine-Hugoniot condition n...

The size of the shock-layer governed by a conservation law is studied. The conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum-principle arguments. The bounding functions demonstrate that t...

We propose a new numerical 2-point flux for quasilinear convection–diffusion equation. This is shown to be an approximation of the derived from solution two-point Dirichlet boundary value problem projection continuous onto line connecting neighboring collocation points. The later approach generalizes idea first proposed by Scharfetter and Gummel [IEEE Trans. Electron Devices 16 (19...