Numerical solution of some quasilinear singularly perturbed heat-conduction equations on nonuniform grids

Numerical methods of solving quasilinear heat-conduction equations with a small parameter for the highest-order derivatives with respect to the spatial variables are considered. Nonlinear difference schemes are constructed by the exact difference scheme method. The proposed schemes are uniformly convergent in the small parameter on arbitrary nonuniform grids. Iterative algorithms uniformly convergent in the small parameter are chosen for solving the nonlinear difference schemes.