Legendre Collocation Spectral Method for Solving Space Fractional Nonlinear Fisher’s Equation

Liu, Zeting; Lv, Shujuan; Li, Xiaocui

doi:10.1007/978-981-10-2663-8_26

Cited by 2 publications

(1 citation statement)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To solve this problem, various computational approaches have been designed in order to approximate the solutions of continuous (fractional or integral) Fisher's equations. Some approximation techniques have been proposed in the literature to that effect, including finite-difference schemes [15], differential and integral quadrature techniques [16,17], Legendre spectral collocation methods [18], discrete local discontinuous Galerkin methods [19], finite volume schemes with preconditioned Lanczos techniques [20], and homotopy perturbation methods [21]. In most of the cases, the methods proposed are capable of approximating the solutions of the fractional Fisher's equation with a high degree of precision, but the preservation of the most important features of the solutions of interest is neglected.…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics

Macías‐Díaz

2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

We depart from the well-known one-dimensional Fisher’s equation from population dynamics and consider an extension of this model using Riesz fractional derivatives in space. Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered differences. The fully discrete population model is implicit and linear, so a convenient vector representation is readily derived. Under suitable conditions, the matrix representing the implicit problem is an inverse-positive matrix. Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions. Moreover, the computational solubility of the discrete model is tackled in the closing remarks.

show abstract

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics

Macías‐Díaz

2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients

Liu

Lü

2017

International Journal of Nonlinear Sciences and Numerical Simulation

View full text Add to dashboard Cite

Abstract:We consider the initial value problem of the time fractional diffusion equation on the whole line and the fractional derivative is described in Caputo sense. A fully discrete Hermite pseudospectral approximation scheme is structured basing Hermite-Gauss points in space and finite difference in time. Unconditionally stability and convergence are proved. Numerical experiments are presented and the results conform to our theoretical analysis.

show abstract

Legendre Collocation Spectral Method for Solving Space Fractional Nonlinear Fisher’s Equation

Cited by 2 publications

References 22 publications

Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics

Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics

Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients

Contact Info

Product

Resources

About