The Analytical and a Higher-Accuracy Numerical Solution of a Free Boundary Problem in a Class of Discontinuous Functions

摘要

A new method is suggested for obtaining the exact andnumerical solutions of the initial-boundary value problem for a nonlinearparabolic type equation in the domain with the free boundary. With this aim, a special auxiliary problem having some advantagesover the main problem and being equivalent to the main problem ina definite sense is introduced. The auxiliary problem allows us toobtain the weak solution in a class of discontinuous functions. Moreover,on the basis of the auxiliary problem a higher-resolution numericalmethod is developed so that the solution accurately describes allphysical properties of the problem. In order to extract the significanceof the numerical solutions obtained by using the suggested auxiliaryproblem, some computer experiments are carried out.