Application of the Wavelet Galerkin Method to Solution of Nonlinear Bifurcation Problems

ZHANG Lei; TANG Conggang; WANG Dequan; LIU Bing

doi:10.21656/1000-0887.410085

Volume 42 Issue 1

Jan. 2021

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Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(1): 27-35

ZHANG Lei, TANG Conggang, WANG Dequan, LIU Bing. Application of the Wavelet Galerkin Method to Solution of Nonlinear Bifurcation Problems[J]. Applied Mathematics and Mechanics, 2021, 42(1): 27-35. doi: 10.21656/1000-0887.410085

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Application of the Wavelet Galerkin Method to Solution of Nonlinear Bifurcation Problems

doi: 10.21656/1000-0887.410085

¹College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, P.R.China;²Hubei Sanjiang Aerospace Hongyang Electromechanical Co. Ltd., Xiaogan, Hubei 432000, P.R.China

Received Date: 2020-03-25
Rev Recd Date: 2020-05-06
Publish Date: 2021-01-01

Abstract

Abstract

Application of the wavelet Galerkin method to solution of nonlinear bifurcation problems was studied through a typical Bratu problem. Firstly, 1D and 2D Bratu equations were discretized with the Coiflet based wavelet Galerkin method, then both the pseudo arclength scheme for tracing solution curves and the extended equations for calculating limit bifurcation points were derived in the case of 1parameter Bratu problems, similarly both the pseudo arclength scheme for tracing solution surfaces and the extended equations for solving cusp bifurcation points were also derived in the case of 2parameter Bratu problems. Numerical results show that, the wavelet Galerkin method not only has higher accuracy during bifurcation point calculation, but also is capable of capturing fold lines and cusp catastrophe quantitatively in the case of 2parameter bifurcation problems. This example exhibits the specific procedure of numerical bifurcation analysis based on the wavelet Galerkin method and demonstrates its potential for capturing complex bifurcation behaviors of multiparameter problems.
- wavelet Galerkin method,
- bifurcation computation,
- 2parameter problem,
- cusp catastrophe

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References(20)

References

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