# An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

Molati, Motlatsi; Murakawa, Hideki

- Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 305-314

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topMolati, Motlatsi, and Murakawa, Hideki. "An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 305-314. <http://eudml.org/doc/294897>.

@inProceedings{Molati2017,

abstract = {This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and make it possible to realize the much faster computation rather than the nonlinear schemes with the same level of accuracy. In this paper, numerical experiments are carried out to demonstrate efficiency of the proposed scheme.},

author = {Molati, Motlatsi, Murakawa, Hideki},

booktitle = {Proceedings of Equadiff 14},

keywords = {Stefan problem, Porous medium equation, Cross-diffusion system, Degenerate convection-reaction-diffusion equation, Linear scheme, Error estimate, Numerical method},

location = {Bratislava},

pages = {305-314},

publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},

title = {An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems},

url = {http://eudml.org/doc/294897},

year = {2017},

}

TY - CLSWK

AU - Molati, Motlatsi

AU - Murakawa, Hideki

TI - An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

T2 - Proceedings of Equadiff 14

PY - 2017

CY - Bratislava

PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing

SP - 305

EP - 314

AB - This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and make it possible to realize the much faster computation rather than the nonlinear schemes with the same level of accuracy. In this paper, numerical experiments are carried out to demonstrate efficiency of the proposed scheme.

KW - Stefan problem, Porous medium equation, Cross-diffusion system, Degenerate convection-reaction-diffusion equation, Linear scheme, Error estimate, Numerical method

UR - http://eudml.org/doc/294897

ER -

## References

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- Murakawa, H., An efficient linear scheme to approximate nonlinear diffusion problems, , to appear in Jpn. J. Ind. Appl. Math., DOI: 10.1007/s13160-017-0279-3. MR3768238
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