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Fibonacci-Horner decomposition of the matrix exponential and the fundamental system of solutions. (English) Zbl 1108.65073

Using a standard computation, the authors obtain the basic Fibonacci-Horner basis, as well as the relationship between the matrix exponential and the system of fundamental solutions of an associated scalar linear differential equation of order \(r\). The problem is to compute explicitly the dynamical solution and the fundamental system of solutions of this dynamical equation. The decomposition of \(e^{tA}\) in some important situations is also studied. Some examples are discussed.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A30 Linear ordinary differential equations and systems
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