TOM: Solve two-point boundary value problems for ODEs using the Top Order Method of order 2 and 6. Nonlinear problems are solved using quasilinearization. Mesh selection is based on the conditioning of the discrete linear problems. [1,2,3,4,5,6,7].
The code TOM consists of four files:
- tom.m contains the functions that implement the integration procedure;
- tominit.m Form the initial guess for TOM.
- tomget.m Get TOM OPTIONS parameters.
- tomset.m Set TOM OPTIONS parameters.
If you retrieve the software, please send a message to mazzia@dm.uniba.it so that we may keep you updated on any changes. Also any bug reports are appreciated.
The code has been tested on many difficult stiff test problems. For example, those contained in the Cash's home page.
Read also the slides of SCICADE 03 and the report n. 36/2003 for more information about the mesh selection strategy used in TOM.
[2] L. Brugnano and D. Trigiante, A New Mesh Selection Strategy for ODEs,Appl. Numer. Math. (1997), 24, 1-21.
[3] F. Mazzia, I. Sgura, Numerical Approximation of Nonlinear BVPs by means of BVMs, Appl. Numer. Math.,42(2002), 337--352.
[5] F. Mazzia, D. Trigiante, A Hybrid Mesh Selection Strategy Based on Conditioning for Boundary Value ODE Problems, Numerical Algorithms, 36 (2004), no.2, 169--187.
[6] L.Aceto and F. Mazzia and D. Trigiante, On the performance of the code Tom on difficult boundary value problems, Oberwolfach Conference Proceedings of the Sixth International Conference on Difference Equations Augsburg, Germany 2001: New Progress in Difference Equations, Ed. Bernd Aulbach; Saber Elaydi; Gerasimos Ladas, 2004.
[7] J. Cash, F. Mazzia, N. Sumarti, D. Trigiante, The Role of Conditioning in Mesh Selection Algorithms for First Order Systems of Linear Two-Point Boundary Value Problems} Journal of Computational Methods in Sciences and Engineering, to appear.
29/10/97