An Approach to Improving the Accuracy and Efficiency of the ROMB Method for Solving the Nonstationary Heat Equation

A modification of the ROMB method for the numerical solution of nonstationary nonlinear heat equations is presented. The modified difference schemes are conservative and, on smooth solutions, provide a second-order approximation in time and space for model differential equations with constant coefficients. For the modified difference schemes, the first differential approximations are given, which make it possible to estimate the truncation errors of the schemes.