Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach
DOI10.1016/j.camwa.2016.04.038zbMath1359.65199OpenAlexW2442403043MaRDI QIDQ520840
Mehdi Dehghan, Mostafa Abbaszadeh
Publication date: 6 April 2017
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2016.04.038
fourth-order Runge-Kutta methodelement free Galerkin (EFG) and moving Kriging interpolationGinzburg-Landau model and Brusselator equationGray-Scott model and Allen-Cahn equationmathematical biology and Turing systempredator-prey model with additional food supply to predator
Developmental biology, pattern formation (92C15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A numerical approach to the study of spatial pattern formation in the ligaments of arcoid bivalves
- A hybrid FEM for solving the Allen-Cahn equation
- Steady states solutions of Allen-Cahn equation by computer algebra
- An efficient fully linearized semi-implicit Galerkin-mixed FEM for the dynamical Ginzburg-Landau equations of superconductivity
- Stable large-scale solver for Ginzburg-Landau equations for superconductors
- Stability and Hopf bifurcation for a three-component reaction-diffusion population model with delay effect
- A meshless local Petrov-Galerkin method for the time-dependent Maxwell equations
- Turing instability conditions for growing domains with divergence free mesh velocity
- Global attractor and Kolmogorov entropy of three component reversible Gray-Scott model on infinite lattices
- Coupling of the improved element-free Galerkin and boundary element methods for two-dimensional elasticity problems
- An improved element-free Galerkin method for numerical modeling of the biological population problems
- Numerical simulation of the three dimensional Allen-Cahn equation by the high-order compact ADI method
- A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems
- Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains
- A computational modeling of the behavior of the two-dimensional reaction-diffusion Brusselator system
- An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
- Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
- Numerical solution of two-dimensional reaction-diffusion Brusselator system
- Turing pattern formation for reaction-convection-diffusion systems in fixed domains submitted to toroidal velocity fields
- A moving Kriging interpolation-based element-free Galerkin method for structural dynamic analysis
- Some new solitonary solutions of the modified Benjamin-Bona-Mahony equation
- Exponential time differencing for stiff systems
- Development of a novel meshless Local Kriging (LoKriging) method for structural dynamic analysis
- Numerical study of pattern formation in an extended Gray-Scott model
- A meshless local moving Kriging method for two-dimensional solids
- An efficient and accurate numerical algorithm for the vector-valued Allen-Cahn equations
- Chemical oscillations, waves, and turbulence
- Chemical instabilities and sustained oscillations
- A two-dimensional numerical study of spatial pattern formation in interacting Turing systems
- Reaction and diffusion on growing domains: scenarios for robust pattern formation
- Bifurcations and exact solutions of ac-driven complex Ginzburg-Landau equation
- Numerical study of quantized vortex interaction in complex Ginzburg-Landau equation on bounded domains
- Smoothing schemes for reaction-diffusion systems with nonsmooth data
- A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
- Asymptotic speed of spread and traveling fronts for a nonlocal reaction-diffusion model with distributed delay
- Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
- A meshless local Kriging method for large deformation analyses
- An error estimate in the EFG method
- A boundary point interpolation method for stress analysis of solids.
- Meshless methods: An overview and recent developments
- A moving grid finite element method applied to a model biological pattern generator
- Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods
- The two-dimensional reaction--diffusion Brusselator system: A dual-reciprocity boundary element solution.
- A second-order scheme for the ``Brusselator reaction-diffusion system
- Spatiotemporal dynamics of reaction-diffusion models of interacting populations
- A novel interpolating element-free Galerkin (IEFG) method for two-dimensional elastoplasticity
- A new compact finite difference scheme for solving the complex Ginzburg-Landau equation
- The local integral equation method for pattern formation simulations in reaction-diffusion systems
- The numerical solution of Cahn-Hilliard (CH) equation in one, two and three-dimensions via globally radial basis functions (GRBFs) and RBFs-differential quadrature (RBFs-DQ) methods
- Meshless simulation of stochastic advection-diffusion equations based on radial basis functions
- Direct meshless local Petrov-Galerkin method for elliptic interface problems with applications in electrostatic and elastostatic
- The diffusion-Brusselator equation
- A novel meshless approach -- Local Kriging (LoKriging) method with two-dimensional structural analysis
- Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method
- Numerical solution of transient heat conduction problems using improved meshless local Petrov-Galerkin method
- Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations
- The locally extrapolated exponential time differencing LOD scheme for multidimensional reaction-diffusion systems
- The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation
- A semi-analytical Fourier spectral method for the Allen-Cahn equation
- The finite volume spectral element method to solve Turing models in the biological pattern formation
- A moving least square reproducing polynomial meshless method
- A meshfree weak-strong (MWS) form method for the unsteady magnetohydrodynamic (MHD) flow in pipe with arbitrary wall conductivity
- The improved element-free Galerkin method for two-dimensional elastodynamics problems
- Uniform attractor of non-autonomous three-component reversible Gray-Scott system
- Efficient time discretization for local discontinuous Galerkin methods
- Second-order implicit-explicit scheme for the Gray-Scott model
- Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
- The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems
- A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains
- A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation
- A Meshless Method for Solving the 2D BrusselatorReaction-Diffusion System
- An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation
- Surfaces Generated by Moving Least Squares Methods
- Element‐free Galerkin methods
- Exact Homoclinic and Heteroclinic Solutions of the Gray--Scott Model for Autocatalysis
- Moving kriging interpolation and element-free Galerkin method
- Fourth-Order Time-Stepping for Stiff PDEs
- Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations
- FURTHER INVESTIGATION OF ELEMENT-FREE GALERKIN METHOD USING MOVING KRIGING INTERPOLATION
- Scattered Data Approximation
- A local point interpolation method for static and dynamic analysis of thin beams
- A real distinct poles exponential time differencing scheme for reaction-diffusion systems