The comparison between the DRBEM and DQM solution of nonlinear reaction–diffusion equation

Meral, Gülnihal; Tezer‐Sezgin, M.

doi:10.1016/j.cnsns.2011.02.008

Cited by 15 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From this equation, a repetition formula for the calculation of coefficients is supplied, while coefficients in fractional PS expansion can be calculated repeatedly by repeated fractional differentiation of the truncated residual function. 13,26 The RPSM propose the solution for equations (13) and (14) with a fractional PS at t = 0. 11 Suppose that the solution takes the expansion form…”

Section: Basic Definitions Of Fractional Calculus Theorymentioning

confidence: 99%

Solutions of the time fractional reaction–diffusion equations with residual power series method

Tchier

İnç

Körpınar

et al. 2016

Advances in Mechanical Engineering

View full text Add to dashboard Cite

In this article, the residual power series method for solving nonlinear time fractional reaction-diffusion equations is introduced. Residual power series algorithm gets Maclaurin expansion of the solution. The algorithm is tested on Fitzhugh-Nagumo and generalized Fisher equations with nonlinearity ranging. The solutions of our equation are computed in the form of rapidly convergent series with easily calculable components using Mathematica software package. Reliability of the method is given by graphical consequences, and series solutions are used to illustrate the solution. The found consequences show that the method is a powerful and efficient method in determination of solution of the time fractional reaction-diffusion equations.

show abstract

Section: Basic Definitions Of Fractional Calculus Theorymentioning

confidence: 99%

Solutions of the time fractional reaction–diffusion equations with residual power series method

Tchier

İnç

Körpınar

et al. 2016

Advances in Mechanical Engineering

View full text Add to dashboard Cite

show abstract

“…Usually diffusion phenomena are simply simulated by linear Laplace diffusion in much of the previous literature [2,[22][23][24]. However, diffusion behavior is so complicated that the nonlinear reaction-diffusion models were considered in several papers [3,[25][26][27][28]. Very recently, the nonlinear -Laplace diffusion ( > 1) is applied to the simulation of some diffusion behaviors [3].…”

Section: Remarkmentioning

confidence: 99%

LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

Rao

Wang

Zhong

et al. 2013

Journal of Applied Mathematics

View full text Add to dashboard Cite

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

show abstract

“…. ; m, is studied in [1,18,28,37,39], among others. If each of these unknowns represents the concentration of a chemical species, and the equations are coupled in the nonlinear reaction terms, then spatial patterns of chemical concentrations may develop under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

Reprint of Domain decomposition multigrid methods for nonlinear reaction–diffusion problems

Arrarás

Gaspar

Portero

et al. 2015

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

The comparison between the DRBEM and DQM solution of nonlinear reaction–diffusion equation

Cited by 15 publications

References 26 publications

Solutions of the time fractional reaction–diffusion equations with residual power series method

Solutions of the time fractional reaction–diffusion equations with residual power series method

LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

Reprint of Domain decomposition multigrid methods for nonlinear reaction–diffusion problems

Contact Info

Product

Resources

About