THE METHOD OF SOLVING NONLINEAR HEAT TRANSFER MODEL IN FREEZING SOIL

Abstract

The nonlinear model of heat transfer in freezing soil was corrected using the results of experimental studies of other scientists. A nonlinear difference equation is constructed and a priori estimates are obtained for solving nonlinear algebraic equations. The nonlinear difference problem is solved by Newton’s method. The paper also considers the problem of choosing the initial approximation of Newton’s method. Using a priori estimates, the quadratic convergence of the iterative method is proved. Numerical calculations have been performed. A strong discrepancy in results between linear and nonlinear difference problem is shown using graphical representation.