A fast and efficient numerical algorithm for Swift-Hohenberg equation with a nonlocal nonlinearity

DOI10.1016/J.AML.2021.107170OpenAlexW3136999249WikidataQ112880148 ScholiaQ112880148MaRDI QIDQ2233251

Qingqu Zhuang, Shuying Zhai, Yangfang Deng, Zhifeng Weng

Publication date: 15 October 2021

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

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107170

zbMATH Keywords

operator splittingstability and convergenceFourier spectral methodSSP-RK methodnonlocal Swift-Hohenberg equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Integro-partial differential equations (35R09)

Related Items (8)

An unconditionally energy-stable linear Crank-Nicolson scheme for the Swift-Hohenberg equation ⋮ Energy-stable finite element method for a class of nonlinear fourth-order parabolic equations ⋮ Two SAV numerical methods for the nonlocal Cahn-Hilliard-Hele-Shaw system ⋮ Error analysis of a linear unconditionally energy-stable leapfrog scheme for the Swift-Hohenberg equation ⋮ A non-iterative and unconditionally energy stable method for the Swift-Hohenberg equation with quadratic-cubic nonlinearity ⋮ Error estimate of a stabilized second-order linear predictor-corrector scheme for the Swift-Hohenberg equation ⋮ Operator splitting scheme based on barycentric Lagrange interpolation collocation method for the Allen-Cahn equation ⋮ Error analysis of first- and second-order linear, unconditionally energy-stable schemes for the Swift-Hohenberg equation

Cites Work

• Analysis of nonlocal neural fields for both general and gamma-distributed connectivities
• Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation
• Existences of periodic solutions to the generalized Swift-Hohenberg equation on symmetry-breaking model
• Efficient modified techniques of invariant energy quadratization approach for gradient flows
• Numerical simulation of Swift-Hohenberg equation by the fourth-order compact scheme
• On stability of numerical schemes via frozen coefficients and the magnetic induction equations
• The Swift-Hohenberg equation with a nonlocal nonlinearity
• Numerical approximations for a new \(L^2\)-gradient flow based phase field crystal model with precise nonlocal mass conservation
• Convergence of a Fast Explicit Operator Splitting Method for the Epitaxial Growth Model with Slope Selection
• Total variation diminishing Runge-Kutta schemes
• On the Construction and Comparison of Difference Schemes

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