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

DOI10.1080/00207160600961729zbMath1105.65348OpenAlexW2052407723MaRDI QIDQ3423761

Damian Słota, R. Grzymkowski, Mariusz Pleszczyński

Publication date: 15 February 2007

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160600961729

zbMATH Keywords

comparison of methodsnumerical examplesmoving boundary problemStefan problemRunge-Kutta methodfourth-order Runge-Kutta methodadomian decomposition method

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Heat equation (35K05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Free boundary problems for PDEs (35R35)

Related Items (2)

The solution of two-phase inverse Stefan problem based on a hybrid method with optimization ⋮ A new application of He's variational iteration method for the solution of the one-phase Stefan problem

Uses Software

• Mathematica

Cites Work

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• Numerical study of Lorenz's equation by the Adomian method
• A decomposition solution for fins with temperature-dependent surface heat flux
• A review of the decomposition method in applied mathematics
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• The Cauchy problem for the wave equation using the decomposition method
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• Solution of linear and nonlinear parabolic equations by the decomposition method
• An application for linear and nonlinear heat equations by Adomian's decomposition method
• Application of the decomposition method to identify the distributed parameters of an elliptical equation
• Exact solutions to nonlinear diffusion equations obtained by the decomposition method
• Blow-up for solutions of some linear wave equations with mixed nonlinear boundary conditions
• Practical formulae for the calculus of multivariable Adomian polynomials
• The decomposition method for Cauchy advection-diffusion problems
• One-phase inverse Stefan problem solved by Adomian decomposition method
• A New Approach to the Gas Dynamics Equation: An Application of the Decomposition Method
• Decomposition method for nonlinear isothermal magnetostatic atmospheres
• Stefan problem solved by Adomian decomposition method

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