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.

This software is also peer reviewed by journal TOMS.

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

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  1. Molina-Meyer, Marcela; Prieto-Medina, Frank Richard: Pseudospectral versus Galerkin methods: fourth order equations (2022)
  2. Ramos, Higinio; Singh, Gurjinder: Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator (2022)
  3. Amodio, Pierluigi; Arnold, Anton; Levitina, Tatiana; Settanni, Giuseppina; Weinmüller, Ewa B.: On the Abramov approach for the approximation of whispering gallery modes in prolate spheroids (2021)
  4. Amodio, Pierluigi; Budd, Chris J.; Koch, Othmar; Rottschäfer, Vivi; Settanni, Giuseppina; Weinmüller, Ewa: Near critical, self-similar, blow-up solutions of the generalised Korteweg-de Vries equation: asymptotics and computations (2020)
  5. Amodio, Pierluigi; Giordano, Domenico; Iavernaro, Felice; Labianca, Arcangelo; Lazzo, Monica; Mazzia, Francesca; Pisani, Lorenzo: Mathematical aspects relative to the fluid statics of a self-gravitating perfect-gas isothermal sphere (2020)
  6. Amodio, Pierluigi; Settanni, Giuseppina: Numerical strategies for solving multiparameter spectral problems (2020)
  7. Costabile, Francesco Aldo; Caira, Rosanna; Gualtieri, Maria Italia: A block hybrid method for non-linear second order boundary value problems (2019)
  8. Settanni, Giuseppina; Sgura, Ivonne: Devising efficient numerical methods for oscillating patterns in reaction-diffusion systems (2016)
  9. Amodio, P.; Budd, C. J.; Koch, O.; Settanni, G.; Weinmüller, E.: Asymptotical computations for a model of flow in saturated porous media (2014)
  10. Amodio, P.; Levitina, T.; Settanni, G.; Weinmüller, E. B.: Numerical simulation of the whispering gallery modes in prolate spheroids (2014)
  11. Amodio, Pierluigi; Settanni, Giuseppina: A finite differences MATLAB code for the numerical solution of second order singular perturbation problems (2012)
  12. Sgura, Ivonne; Bozzini, Benedetto; Lacitignola, Deborah: Numerical approximation of Turing patterns in electrodeposition by ADI methods (2012)