Solution to the 1D Stefan problem using the Unified Transform Method

In this paper the one-dimensional two-phase Stefan problem is studied analytically leading to a system of non-linear Volterra-integral-equations describing heat distribution in each phase. For unified transform method has been employed which provides via global relation, by these problems can be solved using integral representations. To do this, underlying partial differential equation rewritten into certain divergence form, enables treat boundary values as part integrals. Classical analytical methods fail case due moving interface. From resulting integro-differential equations one for position phase change first step. This done numerically fix-point iteration and spline interpolation. Once obtained, temperature both phases generated from their representation.