numerical study of one-phase stefan-type problems

‎we all know that parabolic equations with non-classical boundary conditions and stefan’s problem have become very popular in recent years due to their many applications in more basic and applied science problems‎. ‎also‎, ‎differential equations with integral conditions have found wide applications in solving chemistry and physics problems‎. ‎many problems that appear in heat transfer can be reduced to non-classical problems with integral conditions‎.‎in this document‎, ‎we first mention the application of stefan’s one-phase problems‎, ‎including the non-classical thermal equation and the integral boundary condition‎, ‎in problems related to chemistry‎. ‎then we examine a numerical technique to solve it and prove the convergence of the method‎.‎finally‎, ‎numerical examples are presented to demonstrate the effectiveness of the method for solving linear and nonlinear diffusion-response equations with these non-classical conditions‎.