A numerical solution of a fractional-order reaction-diffusion model is discussed.With the development of fractional-order differential equations,Schnakenberg model becomes more and more important.However,there are few...A numerical solution of a fractional-order reaction-diffusion model is discussed.With the development of fractional-order differential equations,Schnakenberg model becomes more and more important.However,there are few researches on numerical simulation of Schnakenberg model with spatial fractional order.It is also important to find a simple and effective numerical method.In this paper,the Schnakenberg model is numerically simulated by Fourier spectral method.The Fourier transform is applied to transforming the partial differential equation into ordinary differential equation in space,and the fourth order Runge-Kutta method is used to solve the ordinary differential equation to obtain the numerical solution from the perspective of time.Simulation results show the effectiveness of the proposed method.展开更多
This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conforma...This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the solution.Interestingly,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.展开更多
Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approxima...Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.展开更多
基金National Natural Science Foundation of China(No.11361037)。
文摘A numerical solution of a fractional-order reaction-diffusion model is discussed.With the development of fractional-order differential equations,Schnakenberg model becomes more and more important.However,there are few researches on numerical simulation of Schnakenberg model with spatial fractional order.It is also important to find a simple and effective numerical method.In this paper,the Schnakenberg model is numerically simulated by Fourier spectral method.The Fourier transform is applied to transforming the partial differential equation into ordinary differential equation in space,and the fourth order Runge-Kutta method is used to solve the ordinary differential equation to obtain the numerical solution from the perspective of time.Simulation results show the effectiveness of the proposed method.
文摘This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the solution.Interestingly,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.
文摘Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.
