Exponential integrator methods for systems of non-linear space-fractional models with super-diffusion processes in pattern formation

DOI10.1016/j.camwa.2018.02.027zbMath1419.65022OpenAlexW2791262273WikidataQ115580766 ScholiaQ115580766MaRDI QIDQ2001321

Bruce A. Wade, Olaniyi Samuel Iyiola

Publication date: 3 July 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.02.027

zbMATH Keywords

pattern formationreaction-diffusion equationsexponential time differencingRiesz fractional derivativereal distinct poles

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Developmental biology, pattern formation (92C15) Cell biology (92C37) Fractional partial differential equations (35R11)

Related Items (5)

Complex-order fractional diffusion in reaction-diffusion systems ⋮ Wavelets computational modeling of nonlinear coupled reaction–diffusion models arising in chemical processes ⋮ Pattern formation in reaction-diffusion systems on evolving surfaces ⋮ Analytical and approximate solutions of (2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation ⋮ Analytical study of \((3+1)\)-dimensional fractional-reaction diffusion trimolecular models

Uses Software

• mftoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fourier spectral methods for fractional-in-space reaction-diffusion equations
• Devising efficient numerical methods for oscillating patterns in reaction-diffusion systems
• Fractional calculus for scientists and engineers.
• Exponential time differencing for stiff systems
• Reaction-diffusion models for biological pattern formation
• Generalized integrating factor methods for stiff PDEs
• Numerical approximations and padé approximants for a fractional population growth model
• Riesz potential operators and inverses via fractional centred derivatives
• Numerical solutions for fractional reaction-diffusion equations
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• A new class of time discretization schemes for the solution of nonlinear PDEs
• Parallel LOD methods for second order time dependent PDEs
• Finite element solutions for the space fractional diffusion equation with a nonlinear source term
• A novel compact numerical method for solving the two-dimensional non-linear fractional reaction-subdiffusion equation
• The finite volume spectral element method to solve Turing models in the biological pattern formation
• Analysis and applications of the exponential time differencing schemes and their contour integration modifications
• An ETD Crank-Nicolson method for reaction-diffusion systems
• Rational Approximation to the Fractional Laplacian Operator in Reaction-Diffusion Problems
• Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
• An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
• Pattern formation in the one-dimensional Gray - Scott model
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• Functions of Matrices
• A real distinct poles exponential time differencing scheme for reaction-diffusion systems

This page was built for publication: Exponential integrator methods for systems of non-linear space-fractional models with super-diffusion processes in pattern formation