## Abstract

In this paper a modified form of the IMM (Improved Memory Method) for the solution of a nonlinar equation which was proposed by Shacham [Chem. Engng Sci. 44, 1495 (1989)] is presented. The form of IMM presented in the reference uses continued fractions to pass an inverse interpolating polynomial through all the previously calculated points, to find a new estimate for the solution. This method was compared, and found to be superior in terms of function evaluation, to six commonly used methods. Here we present an m-point, globally convergent version of IMM. In this version only m previously calculated points are used to construct the interpolating polynomial, where m can be any number: m ≥ 2, according to the users' choice. A set of 90 test problems, many of them very difficult, were solved using 2-, 3-, 4- and 5-point IMM methods. The proposed method did not fail in any of these cases. It was found that in most cases the 3-point IMM converged must faster, or faster, than the 2-point IMM. The improvements in convergence rate when going to 4- or 5-point IMM from the 3-point one was much more moderate. In a few cases, higher order methods actually required more function evaluations to converge than lower order ones.

Original language | English |
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Pages (from-to) | 621-629 |

Number of pages | 9 |

Journal | Computers and Chemical Engineering |

Volume | 14 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jan 1990 |

## ASJC Scopus subject areas

- General Chemical Engineering
- Computer Science Applications