Software for Boundary Value Problems

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].

The Matlab solver TOM .

Numerical Experiments .

References .

The Matlab solver TOM

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 so that we may keep you updated on any changes. Also any bug reports are appreciated.

Numerical Experiments

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 for more information about the mesh selection strategy used in TOM.


[1] L. Brugnano and D. Trigiante, Solving Differential Problems by Multistep Initial and Boundary Value Methods, Gordon & Breach.

[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.,{\bf 42}(2002), 337--352.

[4] F. Mazzia, D. Trigiante. Mesh selection strategy for Boundary Value Problems. submitted.

[5] L.Aceto and F. Mazzia and D. Trigiante, On the performance of the code Tom on difficult boundary value problems, Oberwolfach Conference Proceedings: Mathematical Modelling Simulation and Optimization of Integrated Electrical Circuits Doc. 01, to appear.

[6] 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}, submitted.

[7] BVMs Bibliography.

This page is maintained by Francesca Mazzia (

Last Update: November 25, 1999