A numerical method for a class of degenerate parabolic equations with Neumann boundary conditions
DU Runmei
PAN Di
NA Yang
Abstract：This paper studies the numerical solution of a class of weakly degenerate parabolic equations with Neumann boundary conditions.To address the singularity problem caused by degenerate boundaries,a novel Galerkin method with self-defined basis functions adapted to the degenerate characteristics is innovatively constructed.By introducing the first term of the basis functions,the computational accuracy of the numerical solution at the degenerate boundary is significantly enhanced.Numerical experiments show that compared with the finite difference method based on the conservation principle(with a maximum error of 1.998 8)and the traditional polynomial basis Galerkin method(with a maximum error of 0.205 01),this method reduces the maximum absolute error to the order with only 4 basis functions,and also greatly reduces the computational time.It is significantly superior to the comparison methods in both accuracy and efficiency,providing an efficient and high-precision tool for solving complex degenerate equations.
Keywords：degenerate parabolic equationsNeumann boundary conditionsGalerkin method
Publication Date：2025-09-15
Online Publishing Date：2025-12-22(First online date of this platform, not the publication date of the document)
Pages：12( 188-199 )