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A numerical method was used to solve a system of diffusion equations of the model.
Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion.
An economic finite difference method for solving the obtained system of diffusion equations is developed and numerical computations of the diffusion processes are carried out.
By linearizing the noise term around the traveling wave solution, we obtain an approximating system of diffusion processes.
In the case of fluctuations around traveling wave solutions, we set up an approximating system of diffusion processes and prove that a well-posed stochastic neural field equation is obtained in the continuum limit.
In order to determine finite-size effects deviations from the mean-field limit due to the finite size of the populations in the network we analyze the fluctuations of this Markov chain and set up an approximating system of diffusion processes.
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Our model is a system of diffusion-based partial differential equations that we use to predict percent transgenic seed at arbitrary distances from a transgenic source under different planting scenarios.
The sapphire tube was connected to a high vacuum system, consisting of diffusion and turbo-molecular pumps.
Gel distributions from large time intervals (6 12 hours) between gel insertion and imaging cannot currently be studied with the fluorimetry system because of diffusion of the fluorophore from the gel to the tissue.
The spectral dimension is discretized into a finite number of intervals leading to a system of multigroup diffusion equations.
The method is illustrated by numerical computation of the solutions to a system of reaction diffusion equations modeling the gasless combustion of a solid fuel.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com