Comparison of Boundedness of Solutions of Differential and Difference Equations
[ 1 ] Instytut Matematyki, Wydział Elektryczny, Politechnika Poznańska | [ P ] employee
2014
chapter in monograph
english
- differential equation
- difference equation
- recurrence
- linear
- third order
- bounded solution
EN In mathematics and computer science, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. Such algorithm usually is a recurrence relation. The difference equation, is an equation which defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. Most algorithms can be directly implemented by computer programs; any other algorithms can at least in theory be simulated by computer programs. In the this paper we are looking on the differences between asymptotic properties of solutions of the difference equation and its continuous analogies on example of third order linear homogeneous differential and difference equations with constant coefficients.We take the both equations with the same characteristic equation. We show that these equations (differential and difference) can have solutions with different properties concerning boundedness.
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