A heat polynomial method for inverse cylindrical one-phase Stefan problems

In this paper, solutions of one-phase inverse Stefan problems are studied. The approach presented in the paper is an application heat polynomials method (HPM) for solving one- and two-dimensional problems, where boundary data reconstructed on a fixed boundary. We present numerical results illustrating several benchmark examples. study effects accuracy measurement error different degree polynomials. Due to ill-conditioning matrix generated by HPM, optimization techniques used obtain regularized solution. Therefore, sensitivity disturbance discussed. Theoretical properties proposed method, as well experiments, demonstrate that reach accurate it quite sufficient consider only few flux problem coefficients solution function found approximately.