Jeff Cash Jeff Cash

Research Interests:

General research interests: numerical analysis
Particular research interests: numerical solution of ODEs Boundary value problems and initial value problems. Geometric Integration.
Click here for the book Solving Differential Equations in R by Karline Soetaert, Jeff Cash and Francesca Mazzia.
Click here to see a list, containing our book, of notable computing books and articles of 2012.
Click here for the BVP software page.
Click here for the IVP software page.
Click here for IVP software – BSD licenced.
Click here for the geometric integration software page. Contains MATLAB and Fortran 90 codes.
Click here for MATLAB Software for Initial Value Problems.
Click here for the Non-Stiff Equations software page. This gives the Cash-Karp Runge-Kutta code in Fortran, Matlab and C.
Click here for the OdePkg software.
Click here for the Fortran 95 version of the IVP software MEBDFI.f. Karline Soetaert Karline Soetaert

Mathematical techniques.

Soetaert, K. & C. Heip, 1990. Sample-size dependence of diversity indices and the determination of sufficient sample size in a high-diversity deep-sea environment. Mar. Ecol. Progr. Ser. 59: 305-307.
Van den Meersche , K., Soetaert, K., Van Oevelen, D., 2009. xsample: an R function for sampling over- and underdetermined linear inverse problems. Journal of Statistical Software, Code Snippets 30(1), 1-15. url
Soetaert, K., Gregoire, M.L., 2011. Data assimilation of the carbonate pH system – a kalman filter tested. Ecol. Modelling 222, 1929-1942.
Soetaert, K., Cash, J.R., Mazzia, F., 2012. Solving differential equations in R. UseR, Springer, 248 pp. web.

Ever since the very beginning of my scientific work, I have been intrigued by mathematical techniques. As a very young scientist (Soetaert and Heip, 1990) I used monte carlo simulation to show that diversity estimates should be used with caution due to their dependence on sample size. Much later I worked on mathematical methods to sample underdetermined linear systems (van den Meersche et al., 2009), or investigated the usability of data assimilation techniques in aquatic systems (Soetaert and Gregoire, 2011). The most extreme example of my work in the field of mathematics, however, is my last book (Soetaert et al., 2012). This deals with both the theory of numerically solving differential equations and their implementation in the software R. I wrote the R example chapters, but also two theoretical chapters – I leave it to the reader to guess which. Mayya Tokman Mayya Tokman


A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
M. Tokman, Journal of Computational Physics, 230 (2011) 8762-8778.

New adaptive exponential propagation iterative Runge-Kutta- type (EPIRK) methods
M. Tokman, P. Tranquilli, and J. Loffeld. Submitted, 2011.

Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs.
J. Loffeld and M. Tokman. Submitted, 2010.

Efficient design of exponential-Krylov integrators for large scale computing
M. Tokman and J. Loffeld. Proceedings of the 10th International Conference on Computational Science, Procedia Computer Science, 1(1), pp. 229-237, (2010).

Computational aspects of mucus propulsion by cilated epithelium
R. Chatelin, P. Poncet and M. Tokman, Proceedings of the 2nd European Conference on Microfluidics, Toulouse 2010.

Automated assessment of short free-text responses in computer science using latent semantic analysis
R. Klein, A. Kyrilov & M. Tokman, ITiCSE’ 11 Proceedings of the 16th annual joint conference on Innovation and technology in computer science education, 158-162, Darmstadt (2011).

Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods
M. Tokman, Journal of Computational Physics 213 (2006) 748–776.

Three-dimensional Model of the Structure and Evolution of the Coronal Mass Ejections
M. Tokman, P. Bellan, Astrophysical Journal, 567(2), pp. 1202, 2002.

Investigations into the Relationship between Spheromak, Solar and Astrophysical Plasmas
P.M. Bellan, S.C. Hsu, J.F. Hansen, M. Tokman, S.E. Pracko, C.A. Romero-Talamas, Proceedings on 19th International Atomic Energy Agency Fusion Energy Conference, Lyon, 2002.

Kirsten Meeker, M.S. Physics & Computer Science

Kirsten Meeker, M.S. Physics & Computer Science

CS Masters Thesis: Digital Filter Stepsize Control of DASPK and its Effect on Control Optimization Performance

A new digital filter stepsize controller was implemented in the large-scale differential-algebraic equation solver DASPK3.1mod. The stepsize controller was taken from a modification to DASSL by S¨oderlind and Wang[21, 20], who investigated the effect of digital filter stepsize control on the computational stability of DASSL. We first tested the performance of DASPK3.1mod while solving several difficult problems, and then measured the effect of its improved computational stability on applications which use the differential-algebraic equation solver for sensitivity analysis and control optimization. We found that the new stepsize controller can substantially reduce the number of iterations needed by the optimizer. We conjecture that the performance improvement is due to the smoother behavior of the solution components with respect to perturbation of the problem parameters.