Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics
Applied and Computational Mathematics
Volume 3, Issue 5, October 2014, Pages: 197-204
Received: Aug. 13, 2014; Accepted: Sep. 11, 2014; Published: Sep. 20, 2014
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Boe-Shong Hong, Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62012, Taiwan
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Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.
Inhomogeneous Boundary Conditions, nD Transfer Function Models, Robin Boundary Conditions, Sturm-Liouville Systems
To cite this article
Boe-Shong Hong, Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics, Applied and Computational Mathematics. Vol. 3, No. 5, 2014, pp. 197-204. doi: 10.11648/j.acm.20140305.12
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