A Class of Diagonally Dominant Implicit Schemes with Arbitrary Numerical Dissipation

Summary

A class of implicit finite difference schemes are proposed for time dependent solution of an unsteady partial differential equation. These schemes are temporally inconsistent to the PDE, only in the steady state, the difference equations become consistent to the steady state differential equation. The coefficient matrix of difference equations is tridiagonal and always diagonally dominant. An important feature of these schemes is that arbitrary amount of numerical dissipation can be incorporated in difference equations by virtue of difference formulas. Calculations with nonlinear Burgers’ equation show fast convergence.