COMPARISON OF NUMERICAL MODELING METHODS FOR QUASI-STEADY PROCESS IN CONDUCTING NONDISPERSIVE MEDIUM WITH RELAXATION

E. A. Bogatyreva

Abstract


This article deals with different numerical methods of solving the Dirichlet-Cauchy problem for equation modeling the quasi-steady process in conducting nondispersive medium with relaxation. Known proofs of existence and uniqueness of solution to this problem are not constructive. Therefore the necessity of selection the appropriate numerical method arises. Such method should allow us to find a solution of the considered problem in the reasonable time. The comparative analysis of the Galerkin method and the method of straight lines with $\varepsilon$-embedding method and complex Rosenbrock method is performed in the article. The results of numerical experiments for one-dimensional case are shown.


Keywords


Galerkin method, Rosenbrock method, quasi-linear Sobolev type equation, weak generalized solution, numerical modeling.

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References


Korpusov M.O., Pletner Yu.D., Sveshnikov A.G. On Quasi-Steady Processes in Conducting Nondispersive Media Computational Mathematics and Mathematical Physics, 2000, vol. 40, no 8, pp. 1237-1249. (in Russian)

Korpusov M.O. Blowup of the Solution to a Pseudoparabolic Equation with the Time Derivative of a Nonlinear Elliptic Operator Computational Mathematics and Mathematical Physics, 2002, vol. 42, no 12, pp. 1788-1795. (in Russian)

Bogatyreva E.A. Numerical Modeling of Quasi-Steady Process in Conducting Nondispersive Medium with Relaxation. Journal of Computational and Engineering Mathematics, 2015, vol. 2, no 1, pp. 45-51. doi: 10.14529/jcem150105

Sveshnikov A.G., Al'shin A.B., Korpusov M.O. The Nonlinear Functional Analysis and Its Applications to Partial Differential Equations. Moscow, Nauchnyi mir Publ., 2008. (in Russian)

Al'shin A.B., Al'shina E.A., Kalitkin N.N., Koryagina A.B. Rosenbrock Schemes with Complex Coefficients for Stiff and Differential Algebraic Systems. Computational Mathematics and Mathematical Physics, 2006, vol. 46, issue 8, pp. 1320-1340.


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