Annotation

Differential equations with piecewise constant argument describe various phenomena, e.g., in biology, mechanics and electronics. Here we study a special case of these equations, namely, a system of equations of the form u1'=F1([t],u1([t]),u2([t]))+g1(t), u2'=F2([t],u1([t]),u2([t]))+g2(t), where [t] stands for the greatest integer function and F1, F2, g1 and g2 are continuous functions. Our program is designed to find the solution of such system on the interval [t0, t0+n] if the initial condition u1(t0)=u10, u2(t0)=u20 is given. The solution is found stepwise - on each interval [t0+i-1, t0+i], i=1,...,n, separately. The values of the solution at chosen points can be computed. Further, the graph of the solution can be shown - the user can choose between several types of graphs (u1 or/and u2 in 2D, a 3D curve or a phase portrait).

Technical Info

The software will launch in a separate window. Java (free) must be installed on a client computer. When launching the software the browser might display a security warning and ask whether to block a potentially dangerous content. Click No (i.e. don't block).

When closing the software we recommend to close the browser tab that opened it. When closing the application itself (not the browser tab), the browser might attempt to recover the tab which might result in the browser crash. You can prevent this by disabling the automatic crash recovery feature of your browser.

Licence Agreement

You may use the software for research and scientific activities free of charge. In all other cases contact RNDr. M. Novák, Ph.D., Vysoké učení technické v Brně, UMAT FEKT, Technická 8, 616 00 Brno, email: novakm@feec.vutbr.cz, phone: 541143135.

Authors and Acknowledgement

I. Hlavičková, M. Klimešová supported by FEKT-S-14-2200 "Reprezentace řešení dynamických systémů, numerické algoritmy řešení"