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Enhanced Euler's method to a free boundary porous media flow problem
Author(s) -
Zhang Jianying,
Jiang Bin
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20691
Subject(s) - backward euler method , euler's formula , euler method , mathematics , runge–kutta methods , convergence (economics) , rate of convergence , ode , residual , porous medium , semi implicit euler method , boundary value problem , euler equations , mathematical analysis , boundary (topology) , numerical analysis , porosity , computer science , algorithm , computer network , channel (broadcasting) , economics , economic growth , geotechnical engineering , engineering
We study an ODE‐based iterative method, the residual velocity method, for steady state free boundary problems. The convergence analysis of the method, as well as the numerical implementation based on Euler's method were provided by Donaldson and Wetton (J Appl Math 71 (2006), 877–897). In this article, we develop an enhanced Euler's method which is nearly as simple as the modified Euler's method but can achieve a rapid convergence rate similar to the fourth‐order Runge‐Kutta method. Numerical results are also provided to verify the validity of our method. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012