scholarly journals Existence and Uniqueness of Solution of an Uncertain Characteristic Cauchy Reaction-Diffusion Equation by Adomian Decomposition Method

2010 ◽  
Vol 15 (3) ◽  
pp. 404-419
Author(s):  
H. Rouhparvar ◽  
S. Abbasbandy ◽  
T. Allahviranloo
Keyword(s):  
Diffusion Equation ◽  
Existence And Uniqueness ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Reaction Diffusion ◽  
Uniqueness Of Solution ◽  
Reaction Diffusion Equation ◽  
Adomian Decomposition

On the Hybrid of Fourier Transform and Adomian Decomposition Method for the Solution of Nonlinear Cauchy Problems of the Reaction-Diffusion Equation

2012 ◽  
Vol 67 (6-7) ◽  
pp. 355-362 ◽  
Author(s):  
Salman Nourazar ◽  
Akbar Nazari-Golshan ◽  
Ahmet Yıldırım ◽  
Maryam Nourazar
Keyword(s):  
Cauchy Problem ◽  
Exact Solution ◽  
Fourier Transform ◽  
Diffusion Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Adomian Decomposition ◽  
The Cauchy Problem

The physical science importance of the Cauchy problem of the reaction-diffusion equation appears in the modelling of a wide variety of nonlinear systems in physics, chemistry, ecology, biology, and engineering. A hybrid of Fourier transform and Adomian decomposition method (FTADM) is developed for solving the nonlinear non-homogeneous partial differential equations of the Cauchy problem of reaction-diffusion. The results of the FTADM and the ADM are compared with the exact solution. The comparison reveals that for the same components of the recursive sequences, the errors associated with the FTADM are much lesser than those of the ADM. We show that as time increases the results of the FTADM approaches 1 with only six recursive terms. This is in agreement with the physical property of the density-dependent nonlinear diffusion of the Cauchy problem which is also in agreement with the exact solution. The monotonic and very rapid convergence of the results of the FTADM towards the exact solution is shown to be much faster than that of the ADM

scholarly journals Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Tianlong Shen ◽  
Jianhua Huang ◽  
Jin Li
Keyword(s):  
Fixed Point ◽  
Diffusion Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Banach Fixed Point Theorem ◽  
Fractional Operator ◽  
Initial Value ◽  
Delayed Reaction

The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays.

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