Stability and numerical approximation for a spacial class of semilin-ear parabolic equations on the Lipschitz bounded regions: Sivashin-sky equation

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Mesrizedeh Mehdi; Shanazari Kamal

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Journal Paper

Paper Information

Journal: Computational Methods for Differential Equations Year:2019 | Volume:7 | Issue:4 (Special Issue) Page(s): 589-600

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Title

Stability and numerical approximation for a spacial class of semilin-ear parabolic equations on the Lipschitz bounded regions: Sivashin-sky equation

Author(s)

Mesrizedeh Mehdi | Shanazari Kamal | Issue Writer Certificate

Keywords

Eigenvalue

Eigenfunction

Galerkin meshless method

Sivashinsky equation

Stability

Abstract

This paper aims to investigate the Stability and numerical approximation of the Sivashinsky equations. We apply the Galerkin meshfree method based on the radial basis functions (RBFs) to discretize the spatial variables and use a group presenting scheme for the time discretization. Because the RBFs do not generally vanish on the boundary, they can not directly approximate a Dirichlet boundary problem by Galerkin method. To avoid this di culty, an auxiliary parametrized technique is used to convert a Dirichlet boundary condition to a Robin one. In addition, we extend a Stability theorem on the higher order elliptic equations such as the bihar-monic equation by the Eigenfunction expansion. Some experimental results will be presented to show the performance of the proposed method.

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APA: Copy

Mesrizedeh, Mehdi, & Shanazari, Kamal. (2019). Stability and numerical approximation for a spacial class of semilin-ear parabolic equations on the Lipschitz bounded regions: Sivashin-sky equation. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 7(4 (Special Issue)), 589-600. SID. https://sid.ir/paper/345701/en

Vancouver: Copy

Mesrizedeh Mehdi, Shanazari Kamal. Stability and numerical approximation for a spacial class of semilin-ear parabolic equations on the Lipschitz bounded regions: Sivashin-sky equation. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS[Internet]. 2019;7(4 (Special Issue)):589-600. Available from: https://sid.ir/paper/345701/en

IEEE: Copy

Mehdi Mesrizedeh, and Kamal Shanazari, “Stability and numerical approximation for a spacial class of semilin-ear parabolic equations on the Lipschitz bounded regions: Sivashin-sky equation,” COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol. 7, no. 4 (Special Issue), pp. 589–600, 2019, [Online]. Available: https://sid.ir/paper/345701/en

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