ON AN APPROACH TO IMPROVING THE ACCURACY AND EFFICIENCY OF THE ROMB METHOD FOR SOLVING THE UNSTEADY HEAT CONDUCTION EQUATION

A modification of the ROMB method is presented for numerically solving unsteady nonlinear heat conduction equations. The modified difference schemes are conservative and, for smooth solutions, approximate the model differential equations with constant coefficients with second-order accuracy in both time and space. First differential approximations are provided for the modified difference schemes, enabling the assessment of approximation errors in the schemes.