2023/11/16 by Roman Chapko, Chapko, Roman, Leonidas Mindrinos +1
Computer Science · Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #Digital Filter Design and Implementation #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2311.10192
openalex publication_date 2023/11/16 · openalex created_date 2023/11/21 · openalex updated_date 2026/07/28
In this study, we consider the numerical solution of the Neumann initial boundary value problem for the wave equation in 2D domains. Employing the Laguerre transform with respect to the temporal variable, we effectively transform this problem into a series of Neumann elliptic problems. The development of a fundamental sequence for these elliptic equations provides us with the means to introduce modified double layer potentials. Consequently, we are able to derive a sequence of boundary hypersingular integral equations as a result of this transformation. To discretize the system of equations, we apply the Maue transform and implement the Nyström method with trigonometric quadrature techniques. To demonstrate the practical utility of our approach, we provide numerical examples.