DAFNE swMATH ID: 4453 Software Authors: Aluffi-Pentini, Filippo; Parisi, Valerio; Zirilli, Francesco Description: 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).] Homepage: http://dl.acm.org/citation.cfm?id=1632 Programming Languages: Fortran Keywords: iterative methods; differential-equations algorithm; DAFNE; FORTRAN subprograms Related Software: CUTE; CUTEr; iPiano; iPiasco; LSODE; Pascal-SC; Y12M; HOMPACK; KELLEY; DFO; PITCON Cited in: 12 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A differential-equations algorithm for nonlinear equations. Zbl 0546.65034Aluffi-Pentini, Filippo; Parisi, Valerio; Zirilli, Francesco 1984 all top 5 Cited by 24 Authors 2 Zirilli, Francesco 1 Ali, Montaz M. 1 Aluffi-Pentini, Filippo 1 Alvarez, Felipe 1 Bartholomew-Biggs, Michael C. 1 Chen, Caihua 1 Dương Việt Thông 1 Gebrie, Anteneh Getachew 1 Herzel, Stefano 1 Luong Van Long 1 Ma, Shiqian 1 Martínez, José Mario 1 Oliphant, Terry-Leigh 1 Ouyang, Zixiang 1 Parisi, Valerio 1 Recchioni, Maria Cristina 1 Rosa, Bogdan 1 Steihaug, Trond 1 Suleiman, Sara 1 Vu Tien Dung 1 Wang, Lianping 1 Wu, Xinyuan 1 Xia, Jianlin 1 Yang, Junfeng all top 5 Cited in 10 Serials 2 Journal of Optimization Theory and Applications 2 SIAM Journal on Optimization 1 Computers and Fluids 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Numerical Functional Analysis and Optimization 1 Applied Numerical Mathematics 1 Optimization 1 Linear Algebra and its Applications all top 5 Cited in 7 Fields 7 Numerical analysis (65-XX) 7 Operations research, mathematical programming (90-XX) 3 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Field theory and polynomials (12-XX) 1 Ordinary differential equations (34-XX) 1 Fluid mechanics (76-XX) Citations by Year