2007/10/29 by Miklós Antal, Antal, Miklós, Mihály Makai +1
Engineering · Mathematics · Physics and Astronomy · #35C15 #35J15 #Advanced Numerical Methods in Computational Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Numerical methods in engineering #math-ph #math.MP #msc:35C15 #msc:35J15
paper · pdf · doi:10.48550/arxiv.0710.5428
Presentation on SYMMETRY 2007, Kiev
arxiv created 2007/10/29 · openalex publication_date 2007/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem is sought. We associate a group and a graph to that volume. When the group is symmetry of the boundary value problem under investigation, one can specify the structure of the solution, and find out if there are equispectral volumes of a given type. The second technique uses a complex mapping to transplant the solution from volume to volume and a correction function. Equation for the correction function is given. A simple example demonstrates the feasibility of the suggested method.