# Practical Test-Functions Generated by Computer Algorithms

• Ghiocel Toma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3482)

## Abstract

As it is known, Runge-Kutta methods are widely used for numerical simulations [1]. This paper presents an application of such methods (performed using MATLAB procedures) for generating practical test functions. First it is shown that differential equations can generate only functions similar to test functions (defined as practical test functions); then invariance properties of these practical test functions are used for obtaining a standard form for a differential equation able to generate such a function. Further this standard form is used for computer aided generation of practical test-functions; a heuristic algorithm (based on MATLAB simulations) is used so as to establish the most simple and robust expression for the differential equation. Finally it is shown that we obtain an oscillating system (a system working at the limit of stability, from initial null conditions, on limited time intervals) which can be built as an analog circuit using standard electrical components and amplifiers, in an easy manner.

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### References

1. 1.
Kulikov, G.: An advanced version of the local-global step-size control for Runge-Kutta methods applied to index 1 differential algebraic systems. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3037, pp. 565–569. Springer, Heidelberg (2004)
2. 2.
Toma, C.: Acausal pulses in physics-numerical simulations. Bulgarian Journal of Physics (to appear)Google Scholar
3. 3.
D’Avenia, P., Fortunato, D., Pisani, L.: Topological solitary waves with arbitrary charge and the electromagnetic field. Differential Integral Equations 16, 587–604 (2003)
4. 4.
Frankel, M., Roytburd, V.: Finite-dimensional model of thermal instability. Appl. Math. Lett. 8, 39–44 (1995)