Energy method for structure-preserving finite difference schemes and some properties of difference quotient

DOI10.1016/j.cam.2016.08.008zbMath1352.65277OpenAlexW2512911752MaRDI QIDQ730565

Shuji Yoshikawa

Publication date: 28 December 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.08.008

zbMATH Keywords

finite difference methodCahn-Hilliard equationerror estimateexistence of solutionBoussinesq type equationstructure-preserving numerical method

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (10)

Structure-preserving finite difference schemes for the Cahn-Hilliard equation with dynamic boundary conditions in the one-dimensional case ⋮ Structure-preserving finite difference schemes for a semilinear thermoelastic system with second order time derivative ⋮ A structure-preserving scheme for the Allen-Cahn equation with a dynamic boundary condition ⋮ A novel convenient finite difference method for shallow water waves derived by fifth‐order Kortweg and De‐Vries‐type equation ⋮ Structure-preserving finite difference scheme for 1D thermoviscoelastoplastic equations under uniformly distributed temperature ⋮ Energy-conserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions ⋮ Global existence for a semi-discrete scheme of some quasilinear hyperbolic balance laws ⋮ Remarks on energy methods for structure-preserving finite difference schemes -- small data global existence and unconditional error estimate ⋮ A second-order accurate structure-preserving scheme for the Cahn-Hilliard equation with a dynamic boundary condition ⋮ A new conservative finite difference scheme for 1D Cahn-Hilliard equation coupled with elasticity

Cites Work

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• Numerical integration of the Ostrovsky equation based on its geometric structures
• Two energy conserving numerical schemes for the sine-Gordon equation
• New conservative schemes with discrete variational derivatives for nonlinear wave equations
• On the Cahn-Hilliard equation
• Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
• Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
• Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
• Numerical Studies of the Cahn-Hilliard Equation for Phase Separation
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
• Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
• Geometric Numerical Integration
• Analytic semigroups and optimal regularity in parabolic problems
• A stable and conservative finite difference scheme for the Cahn-Hilliard equation
• Finite-difference schemes for nonlinear wave equation that inherit energy conservation property

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