2019/04/02 by Marcela Molina Meyer, Meyer, Marcela Molina, Frank Richard Prieto Medina +1
Engineering · Mathematics · #35J15 #35J25 #35J40 #35J60 #35J91 #65N35 #Analysis of PDEs (math.AP) #Brake Systems and Friction Analysis #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Material Science and Thermodynamics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1904.01337
openalex publication_date 2019/04/02 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
In this paper we present a pseudospectral method in the disk. Unlike the\nmethods known until now, the disk is not duplicated. Moreover, we solve the\nLaplace equation subjected to nonhomogeneous Dirichlet, Neumann and Robin\nboundary conditions and the biharmonic equation subjected to nonhomogeneous\nDirichlet conditions by only using the elements of the corresponding\ndifferentiation matrices. It is worth noting that we don not use any\nquadrature, do not need to solve any decoupled system of ordinary differential\nequations, do not use any pole condition and do not require any lifting. We\nsolve several numerical examples showing that the spectral convergence is being\nmet. The pseudospectral method developed in this paper can be applied to\nestimate Sherwood numbers integrating the mass flux to the disk and it can be\neasily implemented to solve Lotka-Volterra systems and nonlinear problems\ninvolving chemical reactions.\n