An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory

2020 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
Sunil Dutt Purohit ◽  
Aditya Mani Mishra ◽  
Mahesh Bohra
Keyword(s):  
Numerical Approach ◽  
Diffusion Equations ◽  
Multidimensional Diffusion

scholarly journals Stochastic model for multi-term time-fractional diffusion equations with noise

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 287-293
Author(s):  
Vahid Hosseini ◽  
Mohamad Remazani ◽  
Wennan Zou ◽  
Seddigheh Banihashemii
Keyword(s):  
Numerical Solution ◽  
Numerical Approach ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Data Driven ◽  
Algebraic Equations ◽  
Fractional Diffusion Equations ◽  
Collocation Points ◽  
Linear Algebraic Equations ◽  
Collocation Approach

This paper studies a spectral collocation approach for evaluating the numerical solution of the stochastic multi-term time-fractional diffusion equations associated with noisy data driven by Brownian motion. This model describes the symmetry breaking in molecular vibrations. The numerical solution of the stochastic multi-term time-fractional diffusion equations is proposed by means of collocation points method based on sixth-kind Chebyshev polynomial approach. For this purpose, the problem under consideration is reduced to a system of linear algebraic equations. Two examples highlight the robustness and accuracy of the proposed numerical approach.

scholarly journals Local transformations between some nonlinear diffusion equations

1992 ◽  
Vol 33 (3) ◽  
pp. 321-349 ◽  
Author(s):  
J. R. King
Keyword(s):  
Power Law ◽  
Nonlinear Diffusion ◽  
Invariant Solution ◽  
Diffusion Equations ◽  
Similar Form ◽  
Nonlinear Diffusion Equations ◽  
Continuous Transformation ◽  
Group Invariant ◽  
Invariance Properties ◽  
Multidimensional Diffusion

AbstractWe derive local transformations mapping radially symmetric nonlinear diffusion equations with power law or exponential diffusivities into themselves or into other equations of a similar form. Both discrete and continuous transformations are considered. For the cases in which a continuous transformation exists, many additional forms of group-invariant solution may be constructed; some of these solutions may be written in closed form. Related invariance properties of some multidimensional diffusion equations are also exploited.

Computer Simulation of Amperometric Biosensor Response to Mixtures of Compounds

2002 ◽  
Vol 7 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
J. Christensen ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Computer Simulation ◽  
Enzymatic Reaction ◽  
Diffusion Equations ◽  
Response Data ◽  
Finite Difference Technique ◽  
Stationary Diffusion ◽  
Biosensor Array ◽  
Menten Kinetic ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed. The model bases on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The model describes the biosensor response to mixtures of multiple compounds in two regimes of analysis: batch and flow injection. Using computer simulation, large amount of biosensor response data were synthesised for calibration of a biosensor array to be used for characterization of wastewater. The computer simulation was carried out using the finite difference technique.

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