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SIAM Journal on Scientific Computing
Wavelet-Galerkin method for integro-differential equations
Applied Numerical Mathematics
A wavelet-based method for numerical solution of nonlinear evolution equations
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Wavelet methods for PDEs — some recent developments
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A fully adaptive wavelet algorithm for parabolic partial differential equations
Applied Numerical Mathematics
Wavelet-Galerkin method for solving parabolic equations in finite domains
Finite Elements in Analysis and Design
On a wavelet-based method for the numerical simulation of wave propagation
Journal of Computational Physics
A multivariable wavelet-based finite element method and its application to thick plates
Finite Elements in Analysis and Design
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
Journal of Computational Physics
Finite Elements in Analysis and Design
Wavelet-based method for stability analysis of vibration control systems with multiple delays
Computational Mechanics
A second generation wavelet based finite elements on triangulations
Computational Mechanics
Review: Wavelet-based numerical analysis: A review and classification
Finite Elements in Analysis and Design
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This paper presents a modified wavelet approximation for deflections of beams and square thin plates, in which boundary rotational degrees of freedom are included as independent wavelet coefficients. Based on the modified approximations and Hamilton's principle, variational equations for dynamical, statical and buckling problems of square plates are established, without requiring the wavelet approximations or the wavelet basis to satisfy any specific boundary condition in advance. Further, both homogeneous and non-homogeneous boundary conditions, as well as general boundary conditions, of square plates can be treated in the same way as conventional finite element methods' (FEMs') way. These properties are advantages over current wavelet-Galerkin methods and wavelet-FEMs. Illustrative examples are presented at the end of this paper, and the results show that the modified wavelet approximations can achieve satisfactory accuracy for both homogeneous and non-homogeneous boundary conditions of square plates.