Practical Test-Functions Generated by Computer Algorithms
As it is known, Runge-Kutta methods are widely used for numerical simulations . 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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