HOFiD_UP swMATH ID: 6403 Software Authors: Amodio, Pierluigi; Settanni, Giuseppina Description: We show the main features of the MATLAB code HOFiD_UP for solving second order singular perturbation problems. The code is based on high order finite differences, in particular on the generalized upwind method. Within its simplicity, it uses order variation and continuation for solving any difficult nonlinear scalar problem. Several numerical tests on linear and nonlinear problems are considered. The best performances are reported on problems with perturbation parameters near the machine precision, where most of the codes for two-point boundary value problems fail. Homepage: http://dl.acm.org/citation.cfm?id=2240298.2240356 Keywords: adaptive; infrastructure; hybrid; particle-in-cell; PIC; multiscale; asynchronous; discrete-event simulation; DES; event-driven; magnetosphere; dipole Related Software: Matlab; twpbvp; bvptwp.m; bvp4c; COLSYS; acdc; twpbvpl; BvpSolve; diffEq; ALCON; COMSOL; IRKC; COLNEW Cited in: 13 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A finite differences MATLAB code for the numerical solution of second order singular perturbation problems. Zbl 1246.65127Amodio, Pierluigi; Settanni, Giuseppina 2012 all top 5 Cited by 27 Authors 7 Amodio, Pierluigi 7 Settanni, Giuseppina 4 Weinmüller, Ewa B. 2 Budd, Christopher John 2 Koch, Othmar 2 Levitina, Tatiana V. 2 Sgura, Ivonne 1 Arnold, Anton 1 Bozzini, Benedetto 1 Caira, Rosanna 1 Costabile, Francesco Aldo 1 Giordano, Domenico 1 Gualtieri, Maria Italia 1 Iavernaro, Felice 1 Kukreja, Shallu 1 Kukreja, Vijay Kumar 1 Kumari, Archna 1 Labianca, Arcangelo 1 Lacitignola, Deborah 1 Lazzo, Monica 1 Mazzia, Francesca 1 Molina-Meyer, Marcela 1 Pisani, Lorenzo 1 Prieto Medina, Frank Richard 1 Ramos, Higinio 1 Rottschäfer, Vivi 1 Singh, Gurjinder all top 5 Cited in 7 Serials 4 Journal of Computational and Applied Mathematics 3 Applied Mathematics and Computation 1 Computer Physics Communications 1 Physica D 1 Mediterranean Journal of Mathematics 1 Communications in Computational Physics 1 International Journal of Applied and Computational Mathematics all top 5 Cited in 7 Fields 11 Numerical analysis (65-XX) 5 Ordinary differential equations (34-XX) 5 Partial differential equations (35-XX) 2 Fluid mechanics (76-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year