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Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System
In this paper, we systematically study two-species reaction-diffusion-advection system with linear cross-diffusion and cross-advection. Firstly, we...
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High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation
We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty...
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A higher order unconditionally stable numerical technique for multi-term time-fractional diffusion and advection–diffusion equations
Constructing a higher order collocation framework for solving the Caputo multi-term time-fractional advection–diffusion and diffusion-type problems...
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On the Stability of IMEX Upwind gSBP Schemes for 1D Linear Advection-Diffusion Equations
A fully discrete energy stability analysis is carried out for linear advection-diffusion problems discretized by generalized upwind...
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Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity
Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation....
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A Hybridizable Discontinuous Galerkin Method for Magnetic Advection–Diffusion Problems
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection–diffusion problem within a more...
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Spectral variational multi-scale method for parabolic problems: application to 1D transient advection-diffusion equations
In this work, we introduce a variational multi-scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are...
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Stability and bifurcation in a reaction–diffusion–advection predator–prey model
A reaction–diffusion–advection predator–prey model with Holling type-II predator functional response is considered. We show the stability/instability...
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A fully adaptive explicit stabilized integrator for advection–diffusion–reaction problems
A novel second order family of explicit stabilized Runge–Kutta–Chebyshev methods for advection–diffusion–reaction equations is introduced. The new...
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The convergence of high-accuracy three-point compact computational method for structural derivative anomalous diffusion–advection model
A computational method based on compact discretization for solving the nonlinear anomalous diffusion–advection model is proposed via the structural...
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Phytoplankton-chytrid-zooplankton dynamics via a reaction–diffusion–advection mycoloop model
Mycoloop is an important aquatic food web composed of phytoplankton, chytrids (one dominant group of parasites in aquatic ecosystems), and...
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A numerical approach based on Vieta–Fibonacci polynomials to solve fractional order advection–reaction diffusion problem
In this article, we attempt to provide the numerical solution for a non-linear reaction--advection diffusion equation with fractional-order...
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Unsteady suspended sediment distribution in an ice-covered channel through fractional advection–diffusion equation
Despite several applications of the fractional advection–diffusion equation (fADE) in studying sediment transport in an open channel flow, its...
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Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation
A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied. A...
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Lie symmetry analysis and conservation laws for the time fractional generalized advection–diffusion equation
In this paper, the Lie symmetry group method is employed to study the time fractional generalized advection–diffusion equation. The Lie symmetry...
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Global Dynamics of a Lotka–Volterra Competition–Diffusion–Advection Model with Stage Structure
In this paper, we study a classical two species stage structure Lotka–Volterra diffusion–advection system. By employing the Krein–Rutman theorem,...
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Efficient Adaptive Stochastic Collocation Strategies for Advection–Diffusion Problems with Uncertain Inputs
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that...
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Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation
The time-fractional advection–diffusion reaction equation (TFADRE) is a fundamental mathematical model because of its key role in describing various...
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Speed Selection of Traveling Waves of a Reaction–Diffusion–Advection Equation with High-Order Terms
In this paper, we investigate the speed selection mechanism of traveling wave solutions for a reaction–diffusion–advection equation with high-order...