Asymptotic behavior of solutions to linear homogeneous second-order difference equations (Q1972522)
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scientific article; zbMATH DE number 1429628
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic behavior of solutions to linear homogeneous second-order difference equations |
scientific article; zbMATH DE number 1429628 |
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Asymptotic behavior of solutions to linear homogeneous second-order difference equations (English)
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2 August 2000
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The paper presents a complete analysis of asymptotic behavior (as \(n\to\infty\)) of the general solution of the equation \(x_{n+2}=Ax_{n}+Bx_{n+1}\), \(A\neq 0\), \(n=0,1,\ldots\), for various possible \((A,B)\in\mathbb{R}^{2}\) and initial data. A comparison with well-known effects in the behavior of solutions of nonlinear equations is given.
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second-order difference equations
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asymptotic behavior
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general solution
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comparison
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nonlinear equations
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