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Keywords:
fundamental matrix; eigenvalues; linear system of ordinary differential equations; linear differential system; shifted exponentials; the least square method
fundamental matrix; eigenvalues; linear system of ordinary differential equations; linear differential system; shifted exponentials; the least square method
Summary:
Shifting a numerically given function $b_1 \exp a_1t + \dots+ b_n \exp a_n t$ we obtain a fundamental matrix of the linear differential system $\dot{y} =Ay$ with a constant matrix $A$. Using the fundamental matrix we calculate $A$, calculating the eigenvalues of $A$ we obtain $a_1, \dots, a_n$ and using the least square method we determine $b_1, \dots, b_n$.
References:
[1] P. Hartman: Ordinary differential equations. John Wiley & Sons, New York, London, Sydney, 1964. MR 0171038 | Zbl 0125.32102
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