Spectral method for solving the time fractional Boussinesq equation

DOI10.1016/j.aml.2018.06.008zbMath1462.65165OpenAlexW2809594759MaRDI QIDQ1992231

Moli Zhao, Hui Zhang, Rumeng Zheng, Xiao-yun Jiang

Publication date: 2 November 2018

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

Full work available at URL: https://doi.org/10.1016/j.aml.2018.06.008

zbMATH Keywords

Fourier spectral methodstability and convergence analysistime fractional Boussinesq equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Fractional partial differential equations (35R11)

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Cites Work

• Fractional Lie group method of the time-fractional Boussinesq equation
• Space-fractional advection-dispersion equations by the Kansa method
• Applications of density matrix in the fractional quantum mechanics: Thomas-Fermi model and Hohenberg-Kohn theorems revisited
• Numerical analysis of the space fractional Navier-Stokes equations
• A time-space spectral method for the time-space fractional Fokker-Planck equation and its inverse problem
• Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions
• A fully discrete difference scheme for a diffusion-wave system
• Analysis and Approximation of a Fractional Cahn--Hilliard Equation
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method