Solving parabolic and hyperbolic equations by the generalized finite difference method

DOI10.1016/j.cam.2006.10.090zbMath1139.35007OpenAlexW1969161031MaRDI QIDQ2475342

Francisco Ureña, Juan José Benito, Luis Gavete

Publication date: 11 March 2008

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.2006.10.090

zbMATH Keywords

irregular gridsvon Neumann stability criterionexplicit method, truncation error

Mathematics Subject Classification ID

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) Theoretical approximation in context of PDEs (35A35) Finite difference methods applied to problems in solid mechanics (74S20) General theory of PDEs and systems of PDEs with constant coefficients (35E20)

Related Items (68)

Solving third- and fourth-order partial differential equations using GFDM: application to solve problems of plates ⋮ Modelling of the advection–diffusion equation with a meshless method without numerical diffusion ⋮ High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM) ⋮ Stability of perfectly matched layer regions in generalized finite difference method for wave problems ⋮ Shock-induced two dimensional coupled non-Fickian diffusion-elasticity analysis using meshless generalized finite difference (GFD) method ⋮ Shock-induced thermoelastic wave propagation analysis in a thick hollow cylinder without energy dissipation using mesh-free generalized finite difference (GFD) method ⋮ Simulation of two-dimensional sloshing phenomenon by generalized finite difference method ⋮ Generalized finite difference method for two-dimensional shallow water equations ⋮ A meshless generalized finite difference method for inverse Cauchy problems associated with three-dimensional inhomogeneous Helmholtz-type equations ⋮ Numerical solutions of mild slope equation by generalized finite difference method ⋮ Coupled thermoelastic analysis of an FG multilayer graphene platelets-reinforced nanocomposite cylinder using meshless GFD method: a modified micromechanical model ⋮ Generalized multiscale hybridizable discontinuous Galerkin (GMsHDG) method for flows in nonlinear porous media ⋮ A meshless collocation method for solving the inverse Cauchy problem associated with the variable-order fractional heat conduction model under functionally graded materials ⋮ Application of the generalized finite difference method to three-dimensional transient electromagnetic problems ⋮ Theoretical Analyses on Discrete Formulae of Directional Differentials in the Finite Point Method ⋮ Generalized finite difference time domain method and its application to acoustics ⋮ The generalized finite difference method with third- and fourth-order approximations and treatment of ill-conditioned stars ⋮ A domain-decomposition generalized finite difference method for stress analysis in three-dimensional composite materials ⋮ Localized boundary knot method and its application to large-scale acoustic problems ⋮ Distributed source scheme to solve the classical form of Poisson equation using 3-d finite-difference method for improved accuracy and unrestricted source position ⋮ An efficient collocation method for long-time simulation of heat and mass transport on evolving surfaces ⋮ Solving inverse Stokes problems by modified collocation Trefftz method ⋮ A Modified Finite Particle Method: Multi-dimensional elasto-statics and dynamics ⋮ A meshless collocation scheme for inverse heat conduction problem in three-dimensional functionally graded materials ⋮ Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using generalized finite difference method ⋮ Solving second order non-linear parabolic PDEs using generalized finite difference method (GFDM) ⋮ A mesh-free framework for high-order direct numerical simulations of combustion in complex geometries ⋮ High order difference schemes using the local anisotropic basis function method ⋮ A note on the application of the generalized finite difference method to seismic wave propagation in 2D ⋮ Application of the generalized finite difference method to solve the advection-diffusion equation ⋮ A localized meshless collocation method for bandgap calculation of anti-plane waves in 2D solid phononic crystals ⋮ On the propagation of nonlinear water waves in a three-dimensional numerical wave flume using the generalized finite difference method ⋮ Generalized finite difference method for solving stationary 2D and 3D Stokes equations with a mixed boundary condition ⋮ Improvements to the meshless generalized finite difference method ⋮ Adaptive Solution to Two-Dimensional Partial Differential Equations in Curved Domains Using the Monge--Ampére Equation ⋮ The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems ⋮ Application of a hybrid mesh-free method for shock-induced thermoelastic wave propagation analysis in a layered functionally graded thick hollow cylinder with nonlinear grading patterns ⋮ Solving elliptical equations in 3D by means of an adaptive refinement in generalized finite differences ⋮ Consistency conditions for the influence graphs generalized finite difference method ⋮ Generalized finite difference method for solving two-dimensional non-linear obstacle problems ⋮ Solving Monge-Ampère equation in 2D and 3D by generalized finite difference method ⋮ A GFDM with PML for seismic wave equations in heterogeneous media ⋮ A note on the dynamic analysis using the generalized finite difference method ⋮ A meshless generalized finite difference method for solving shallow water equations with the flux limiter technique ⋮ Generalized finite difference method with irregular mesh for a class of three-dimensional variable-order time-fractional advection-diffusion equations ⋮ Solving anisotropic elliptic and parabolic equations by a meshless method: simulation of the electrical conductivity of a tissue ⋮ A generalized finite difference method based on the peridynamic differential operator for the solution of problems in bounded and unbounded domains ⋮ Solving second order non-linear elliptic partial differential equations using generalized finite difference method ⋮ A hybrid method and unified analysis of generalized finite differences and Lagrange finite elements ⋮ A Conservative Gradient Discretization Method for Parabolic Equations ⋮ A stability analysis for a generalized finite-difference scheme applied to the pure advection equation ⋮ A new high accuracy two-level implicit off-step discretization for the system of three space dimensional quasi-linear parabolic partial differential equations ⋮ A stable noniterative prediction/correction domain decomposition method for hyperbolic problems ⋮ A high accuracy method for long-time evolution of acoustic wave equation ⋮ Generalized finite difference method for a class of multidimensional space-fractional diffusion equations ⋮ Non-linear Fokker-Planck equation solved with generalized finite differences in 2D and 3D ⋮ Generalized finite differences for solving 3D elliptic and parabolic equations ⋮ Error estimates on hybridizable discontinuous Galerkin methods for parabolic equations with nonlinear coefficients ⋮ On elastoplastic analysis of some plane stress problems with meshless methods and successive approximations method ⋮ Generalized finite difference method for solving the double-diffusive natural convection in fluid-saturated porous media ⋮ Solving the telegraph equation in 2-d and 3-d using generalized finite difference method (GFDM) ⋮ Implementations with generalized finite differences of the displacements and velocity-stress formulations of seismic wave propagation problem ⋮ Analysis of elastic wave propagation in a functionally graded thick hollow cylinder using a hybrid mesh-free method ⋮ The use of generalized finite difference method in perfectly matched layer analysis ⋮ On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using generalized finite differences ⋮ Second-order treatment of the interface of domain decomposition method for parabolic problems ⋮ Solving second order non-linear hyperbolic PDEs using generalized finite difference method (GFDM) ⋮ Modeling of laser heating of bi-layered microdomain using the general boundary element method

Cites Work

• Influence of several factors in the generalized finite difference method
• An \(h\)-adaptive method in the generalized finite differences
• Improvements of generalized finite difference method and comparison with other meshless method
• An interpolation method for an irregular net of nodes
• The finite difference method at arbitrary irregular grids and its application in applied mechanics
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Solving parabolic and hyperbolic equations by the generalized finite difference method