## Abstract

The convergence and stability analysis of a "variable" quadratic C^{1}-spline collocation method for solving the initial value problem y^{′}(x)=f(x,y),y(0)=y_{0},x∈[0,b] will be considered. Letting the interior (non-nodal) collocation point x_{k+β}=x_{k}+βh be dependent on some parameter β∈(0,1], it will be shown that the proposed method is strongly unstable if β<12 and it turns out that the method is a continuous extension of the well-known mid-point and trapezoidal methods, if β=12 and β=1, respectively. Moreover, a wider region of absolute stability is achieved if β→1^{-}. Error bounds in the uniform norm for s^{(i)}-y^{(i)},i=0,1 if y∈C^{3}[0,b], together with illustrative examples will also be presented.

Original language | English |
---|---|

Pages (from-to) | 153-160 |

Number of pages | 8 |

Journal | Applied Mathematical Modelling |

Volume | 23 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1999 |

Externally published | Yes |

## Keywords

- 65 D 05
- 65 L 05
- A-stability
- Absolute stability
- Collocation methods
- Initial value problems
- Quadratic spline
- Stiff-equations

## ASJC Scopus subject areas

- Modelling and Simulation
- Applied Mathematics

## Fingerprint

Dive into the research topics of 'One parameter quadratic C^{1}-spline collocation method for solving first order ordinary initial value problems'. Together they form a unique fingerprint.