### Abstract

Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by the Sinc collocation method. The derivatives and integrals are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The error in the approximation of the solution is shown to converge at an exponential rate. Numerical examples are given to illustrate the accuracy and the implementation of the method, the results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are independent of the initial values.

Original language | English |
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Pages (from-to) | 245-255 |

Number of pages | 11 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 137 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 15 2001 |

### Fingerprint

### Keywords

- Fisher's equation
- Nonlinear parabolic equation
- Reaction-diffusion equations

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

**Numerical study of Fisher's reaction-diffusion equation by the Sinc collocation method.** / Al-Khaled, Kamel.

Research output: Contribution to journal › Article

*Journal of Computational and Applied Mathematics*, vol. 137, no. 2, pp. 245-255. https://doi.org/10.1016/S0377-0427(01)00356-9

}

TY - JOUR

T1 - Numerical study of Fisher's reaction-diffusion equation by the Sinc collocation method

AU - Al-Khaled, Kamel

PY - 2001/12/15

Y1 - 2001/12/15

N2 - Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by the Sinc collocation method. The derivatives and integrals are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The error in the approximation of the solution is shown to converge at an exponential rate. Numerical examples are given to illustrate the accuracy and the implementation of the method, the results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are independent of the initial values.

AB - Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by the Sinc collocation method. The derivatives and integrals are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The error in the approximation of the solution is shown to converge at an exponential rate. Numerical examples are given to illustrate the accuracy and the implementation of the method, the results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are independent of the initial values.

KW - Fisher's equation

KW - Nonlinear parabolic equation

KW - Reaction-diffusion equations

UR - http://www.scopus.com/inward/record.url?scp=0035892569&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035892569&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(01)00356-9

DO - 10.1016/S0377-0427(01)00356-9

M3 - Article

AN - SCOPUS:0035892569

VL - 137

SP - 245

EP - 255

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -