A method of fundamental solutions for the one-dimensional inverse Stefan problem

In this paper, solutions of one-phase direct and inverse Stefan problems are presented. The direct problem consists in a calculation of temperature distribution and of a function which describes the position of the moving interface, whilst the inverse problem consists in a calculation of temperature distribution as well as in the reconstruction of the function which describes the temperature distribution on the boundary, when the position of the moving interface is known. The proposed solution is based on the variational iteration method, after the application of which we obtain the solution in the form of continuous functions.

Direct and inverse one-phase Stefan problem solved by the variational iteration method

Analytical and numerical investigation of thermal radiation effects on flow of viscous incompressible fluid with stretchable convergent/divergent channels

The article presents an algorithm of a solution of the two-phase inverse Stefan design problem. Based on the given information about the partial position of a moving interface, a functional was built defining the error of an approximate solution. To find the functional's minimum, a genetic algorithm was used, whereas for solution of the Stefan problem, the alternating phase truncation method was applied. Stability of the procedure was guaranteed using the Tikhonov regularization method. The results obtained corroborate the usefulness of the presented approach.

Solving the inverse Stefan design problem using genetic algorithms

Application of the homotopy perturbation method for the solution of inverse heat conduction problem

In this paper, the solution of one-phase inverse Stefan problem is presented. The problem consists of the reconstruction of the function which describes the distribution of temperature on the boundary, when the position of the moving interface is well-known. The proposed solution is based on the Adomian decomposition method and the least square method.

One-phase inverse stefan problem solved by adomian decomposition method

The solution of the one-phase Stefan problem is presented. This problem consists of finding the distribution of temperature in the domain and the position of the moving interface (freezing front). The proposed solution is based on the Adomian decomposition method and optimalization. The validity of the approach is verified by comparing the results obtained with the analytical solution.

Stefan problem solved by Adomian decomposition method

The solution of the one-phase Stefan problem is presented. A Stefan's task is first approximated with a system of ordinary differential equations. A comparison between the Adomian decomposition method and the fourth-order Runge–Kutta method for solving this system is then presented.

Comparing the Adomian decomposition method and the Runge–Kutta method for solutions of the Stefan problem

Numerical method for multi-phase inverse Stefan design problems

In this paper the approximation method is used to solve the multi-phase inverse Stefan problem. The solution is found in a linear combination form of the functions satisfying the equation of heat conduction. The coefficients of this combination are determined by the least square method for the boundary of a domain. The numerical example is presented.

R. Grzymkowski

Papers

One-phase inverse stefan problem solved by adomian decomposition method

Stefan problem solved by Adomian decomposition method

Comparing the Adomian decomposition method and the Runge–Kutta method for solutions of the Stefan problem

Numerical method for multi-phase inverse Stefan design problems

Multi-phase Inverse Stefan Problems Solved by Approximation Method