A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations

DOI10.1007/s11075-017-0385-yzbMath1420.65087arXiv1705.08057OpenAlexW2619736124MaRDI QIDQ1646670

Pin Lyu, Seak Weng Vong

Publication date: 25 June 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.08057

zbMATH Keywords

finite differencesnonlinear Klein-Gordon equationstime-fractional differential equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) 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) Fractional partial differential equations (35R11)

Related Items

A second-order \(L2\)-\(1_\sigma\) Crank-Nicolson difference method for two-dimensional time-fractional wave equations with variable coefficients, Unconditional convergence in maximum-norm of a second-order linearized scheme for a time-fractional Burgers-type equation, Mixed finite element algorithm for a nonlinear time fractional wave model, A new analytical technique of the \(L\)-type difference schemes for time fractional mixed sub-diffusion and diffusion-wave equations, A nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin–Bona–Mahony‐type equation with nonsmooth solutions, Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation, A fast linearized Galerkin finite element method for the nonlinear multi-term time fractional wave equation, On a second order scheme for space fractional diffusion equations with variable coefficients, A COMPACT DIFFERENCE SCHEME FOR FOURTH-ORDER FRACTIONAL SUB-DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS, Fast evaluation for the two-dimensional nonlinear coupled time-space fractional Klein-Gordon-Zakharov equations, A Linearized Difference Scheme for Time-Fractional Sine-Gordon Equation, Numerical solution of two and three dimensional time fractional damped nonlinear Klein-Gordon equation using ADI spectral element method, Numerical and analytical investigations for neutral delay fractional damped diffusion-wave equation based on the stabilized interpolating element free Galerkin (IEFG) method, A fast linearized numerical method for nonlinear time-fractional diffusion equations, A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations, A novel high order compact ADI scheme for two dimensional fractional integro-differential equations, A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation, A robust preconditioner for two-dimensional conservative space-fractional diffusion equations on convex domains, A high-order method with a temporal nonuniform mesh for a time-fractional Benjamin-Bona-Mahony equation, Finite difference method for time-fractional Klein-Gordon equation on an unbounded domain using artificial boundary conditions, A class of preconditioner for solving the Riesz distributed-order nonlinear space-fractional diffusion equations, DEVELOPMENT AND ANALYSIS OF NEW APPROXIMATION OF EXTENDED CUBIC B-SPLINE TO THE NONLINEAR TIME FRACTIONAL KLEIN–GORDON EQUATION

Uses Software

• FODE

Cites Work

• Unnamed Item
• High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives
• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations
• A new difference scheme for the time fractional diffusion equation
• A circulant preconditioner for fractional diffusion equations
• A fully discrete spectral method for the nonlinear time fractional Klein-Gordon equation
• On nonlinear fractional Klein-Gordon equation
• Numerical solution of sine-Gordon equation by variational iteration method
• Preconditioned iterative methods for space-time fractional advection-diffusion equations
• A compact difference scheme for a two dimensional fractional Klein-Gordon equation with Neumann boundary conditions
• Compact finite difference method for the fractional diffusion equation
• The variational iteration method for studying the Klein-Gordon equation
• A fractional differential equation for a MEMS viscometer used in the oil industry
• The decomposition method for studying the Klein-Gordon equation
• An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations
• A numerical solution of the Klein-Gordon equation and convergence of the decomposition method
• Fractional subequation method for Cahn-Hilliard and Klein-Gordon equations
• A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations
• A high order compact finite difference scheme for time fractional Fokker-Planck equations
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• Finite difference/spectral approximations for the time-fractional diffusion equation
• A high-order exponential ADI scheme for two dimensional time fractional convection-diffusion equations
• A weighted ADI scheme for subdiffusion equations
• Numerical algorithm for the time fractional Fokker-Planck equation
• A fully discrete difference scheme for a diffusion-wave system
• Stochastic solution of space-time fractional diffusion equations
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
• Fourth‐order compact scheme for the one‐dimensional sine‐Gordon equation
• An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
• Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• A high‐order compact scheme for the nonlinear fractional <scp>K</scp>lein–<scp>G</scp>ordon equation
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation