The solution of two-dimensional advection-diffusion equations via operational matrices

DOI10.1016/j.apnum.2013.06.006zbMath1302.65235OpenAlexW1970251122MaRDI QIDQ465091

Francisco de la Hoz, Fernando Vadillo

Publication date: 31 October 2014

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2013.06.006

zbMATH Keywords

advection-diffusion equationsmatrix exponentialsSylvester equationspseudo-spectral methodsChebyshev differentiation matricesHermite differentiation matricesstability: Krylov space

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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A new implementation of the finite collocation method for time dependent PDEs ⋮ An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics ⋮ A reliable numerical algorithm for the fractional vibration equation ⋮ Numerical simulations of time-dependent partial differential equations ⋮ Approximate solution of fractional vibration equation using Jacobi polynomials ⋮ Fast Computing Approaches Based on a Bilinear Pseudo-Spectral Method for Nonlinear Acoustic Wave Equations ⋮ Numerical approximation of the fractional Laplacian on \(\mathbb{R}\) using orthogonal families ⋮ Numerical simulation of the \(N\)-dimensional sine-Gordon equation via operational matrices ⋮ A stable Gaussian radial basis function method for solving nonlinear unsteady convection-diffusion-reaction equations ⋮ A stable method for the evaluation of Gaussian radial basis function solutions of interpolation and collocation problems

Uses Software

• Expokit
• SciPy
• advanpix
• Partial Differential Equation Toolbox
• Differentiation Matrix Suite
• Python

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