A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method. (English) Zbl 1189.65222
The authors propose a numerical method to approximate solutions of diffusion transport equations in one dimensional space. The algorithm combines the B-spline Galerkin method, the Fourier transform and Gauss-Hermite quadrature formulation. The main results of the paper are concerned with the existence, uniqueness and upper error bounds of the solution to the discretized problem. Numerical experiments performed in the final part of the paper support the theoretical findings.
Reviewer: Marius Ghergu (Dublin)
MSC:
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
35K20 | Initial-boundary value problems for second-order parabolic equations |
Keywords:
diffusion transport equation; Galerkin method; Interpolation; Gauss-Hermite quadrature formulation; error bound; algorithm; B-spline; Fourier transform; numerical experimentsReferences:
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