Numerical Solution of Fractional Order Advection Reaction Diffusion Equation with Fibonacci Neural Network

2021 ◽  
Author(s):  
Kushal Dhar Dwivedi ◽  
Rajeev
Keyword(s):  
Neural Network ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Fractional Order ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation

scholarly journals Separation Method of Semi-Fixed Variables Together with Dynamical System Method for Solving Nonlinear Time-Fractional PDEs with Higher-Order Terms

2021 ◽  
Author(s):  
Weiguo Rui
Keyword(s):  
Dynamical System ◽  
Diffusion Equation ◽  
Exact Solutions ◽  
Fractional Order ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
System Method ◽  
Higher Order Terms ◽  
Fractional Models ◽  
Dynamical System Method

Abstract It is well known that methods for solving fractional-order PDEs are grossly inadequate compared with integer-order PDEs. In this paper, a new approach which combined with the separation method of semi-fixed variables and dynamical system method is introduced. As example, a time-fractional reaction-diffusion equation with higher-order terms is studied under the different kinds of fractional-order differential operators. In different parametric regions, phase portraits of systems which derived from the reaction-diffusion equation are presented. Existence and dynamic properties of solutions of this nonlinear time-fractional models are investigated. In some special parametric conditions, some exact solutions of this time-fractional models are obtained. The dynamical properties of some exact solutions are discussed and the graphs of them are illustrated.PACS: 02.30.Jr; 02.30.Oz; 02.70.-c; 02.70.Mv; 02.90.+p; 04.20.Jb; 05.10.-a

scholarly journals Numerical solution of the time fractional reaction–diffusion equation with a moving boundary

2017 ◽  
Vol 338 ◽  
pp. 493-510 ◽  
Author(s):  
Minling Zheng ◽  
Fawang Liu ◽  
Qingxia Liu ◽  
Kevin Burrage ◽  
Matthew J. Simpson
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Moving Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Fractional Reaction

scholarly journals Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

Meccanica ◽  
2020 ◽  
Author(s):  
P. Pandey ◽  
S. Das ◽  
E-M. Craciun ◽  
T. Sadowski
Keyword(s):  
Diffusion Equation ◽  
Present Article ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Linear Algebraic Equations ◽  
Non Linear

AbstractIn the present article, an efficient operational matrix based on the famous Laguerre polynomials is applied for the numerical solution of two-dimensional non-linear time fractional order reaction–diffusion equation. An operational matrix is constructed for fractional order differentiation and this operational matrix converts our proposed model into a system of non-linear algebraic equations through collocation which can be solved by using the Newton Iteration method. Assuming the surface layers are thermodynamically variant under some specified conditions, many insights and properties are deduced e.g., nonlocal diffusion equations and mass conservation of the binary species which are relevant to many engineering and physical problems. The salient features of present manuscript are finding the convergence analysis of the proposed scheme and also the validation and the exhibitions of effectiveness of the method using the order of convergence through the error analysis between the numerical solutions applying the proposed method and the analytical results for two existing problems. The prominent feature of the present article is the graphical presentations of the effect of reaction term on the behavior of solute profile of the considered model for different particular cases.

scholarly journals Numerical approach to the time-fractional reaction-diffusion equation

2019 ◽  
Vol 23 (4) ◽  
pp. 2245-2251 ◽  
Author(s):  
Yu-Yang Qiu
Keyword(s):  
Linear System ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Numerical Results ◽  
Reaction Diffusion Equation ◽  
Fractional Reaction

The numerical solution to the time-fractional reaction-diffusion equation with boundary conditions is considered in this paper. By difference, the problem is transformed to solve a linear system whose coefficient matrices are Toeplitz-like, and the solution can be constructed directly. Numerical results are reported to show the feasibility of the proposed method.

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