### Abstract

Language | English |
---|---|

Pages | 805-826 |

Journal | Nonlinear Analysis: Theory Methods & Applications |

Volume | 52 |

Issue number | 3 |

DOIs | |

Status | Published - Feb 2003 |

### Fingerprint

### Cite this

**Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations.** / Matthies, Karsten.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations

AU - Matthies,Karsten

PY - 2003/2

Y1 - 2003/2

N2 - A numerical method for reaction–diffusion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modified equation, which describes the behavior of the full discretization scheme up to exponentially small errors in the step size. In the construction the numerical scheme is first exactly embedded into a nonautonomous equation. This equation is then averaged with only exponentially small remainder terms. The long-time behavior near hyperbolic equilibria, the persistence of homoclinic orbits and regularity properties are analyzed.

AB - A numerical method for reaction–diffusion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modified equation, which describes the behavior of the full discretization scheme up to exponentially small errors in the step size. In the construction the numerical scheme is first exactly embedded into a nonautonomous equation. This equation is then averaged with only exponentially small remainder terms. The long-time behavior near hyperbolic equilibria, the persistence of homoclinic orbits and regularity properties are analyzed.

UR - http://dx.doi.org/10.1016/S0362-546X(02)00134-7

U2 - 10.1016/S0362-546X(02)00134-7

DO - 10.1016/S0362-546X(02)00134-7

M3 - Article

VL - 52

SP - 805

EP - 826

JO - Nonlinear Analysis: Theory Methods & Applications

T2 - Nonlinear Analysis: Theory Methods & Applications

JF - Nonlinear Analysis: Theory Methods & Applications

SN - 0362-546X

IS - 3

ER -