The Natural Boundary Element Method of the Uniform Transmission Line Equation in 2D Unbounded Region

Fei Teng, Taiying Zhu and Zhixiong Jiang ()
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Fei Teng: College of Arts and Sciences, Shanghai Dianji University, Shanghai 201306, China
Taiying Zhu: College of Arts and Sciences, Shanghai Dianji University, Shanghai 201306, China
Zhixiong Jiang: Commercial College, Shanghai Dianji University, Shanghai 201306, China

Mathematics, 2022, vol. 10, issue 24, 1-16

Abstract: Herein, we are mainly concerned with the natural boundary element (NBE) method of the uniform transmission line (UTL) equation defined in the two-dimensional (2D) boundless region, which has a real physical background. We first create the time semi-discretized scheme of the UTL equation, as well as analyze the convergence and stability for the series of time semi-discretized solutions. Then, we create a fully discretized NBE format by means of a natural boundary reduction and analyze the stability and errors between the fully discretized NBE solutions and the analytical solution. Lastly, we employ two numerical examples to verify the effectiveness of the NBE method.

Keywords: natural boundary element method; uniform transmission line equation; stability and convergence; numerical experiments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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