A differential-equations algorithm for nonlinear equations DAFNE is a set of FORTRAN subprograms for solving nonlinear equations that implements a method founded on the numerical solution of a Cauchy problem for a system of ordinary differential equations inspired by classical mechanics. This paper gives a detailed description of the method as implemented in DAFNE and reports on the numerical tests that have been performed; the DAFNE package is described in the accompanying algorithm. The main conclusions are that DAFNE improves in different substantial respects upon a previous FORTRAN implementation of the same method, and compares favorably with existing software. [The algorithm DAFNE: A differential-equations algorithm for nonlinear equations. ibid. 10, 317-324 (1984).] (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Gebrie, Anteneh Getachew: Dual variable inertial accelerated algorithm for split system of null point equality problems (2021)
  2. Van Long, Luong; Viet Thong, Duong; Dung, Vu Tien: New algorithms for the split variational inclusion problems and application to split feasibility problems (2019)
  3. Ali, M. Montaz; Oliphant, Terry-Leigh: A trajectory-based method for constrained nonlinear optimization problems (2018)
  4. Chen, Caihua; Ma, Shiqian; Yang, Junfeng: A general inertial proximal point algorithm for mixed variational inequality problem (2015)
  5. Steihaug, Trond; Suleiman, Sara: Rate of convergence of higher-order methods (2013)
  6. Wang, Lian-Ping; Rosa, Bogdan: A spurious evolution of turbulence originated from round-off error in pseudo-spectral simulation (2009)
  7. Alvarez, Felipe: Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space (2004)
  8. Wu, Xinyuan; Xia, Jianlin; Ouyang, Zixiang: Note on global convergence of ODE methods for unconstrained optimization (2002)
  9. Martínez, José Mario: Practical quasi-Newton methods for solving nonlinear systems (2000)
  10. Herzel, Stefano; Recchioni, Maria Cristina; Zirilli, Francesco: A quadratically convergent method for linear programming (1991)
  11. Brown, A. A.; Bartholomew-Biggs, M. C.: Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations (1989)
  12. Aluffi-Pentini, Filippo; Parisi, Valerio; Zirilli, Francesco: A differential-equations algorithm for nonlinear equations (1984)