Finite Difference Schemes on Nonuniform Meshes for Parabolic Problems With Generalized Solutions

Boško_S. Jovanović, Peter_P. Matus

We investigate the convergence of finite difference schemes for one dimensional heat conduction equation on nonuniform rectangular meshes. For schemes with averaged right hand sides convergence rate estimates consistent with the smoothness of the solution in discrete $L_2$ norm are obtained. Possible extensions of obtained results are noted.