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Difference Equations
Difference Equations 是動態分析的其中一員。它是「Discrete」,有明顯的 Interval ,通常 t 表示某一段時間(如現在)
, t+1 即是 t 之後一個period ( 那1 的意思表示一個Interval ),如此類推﹔反之,t-1 ,即是 t 之前一個 period ,如此類推。
因此可以用 Δy/Δt 表示。
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First-Order Linear Difference Equations
名稱 | 樣式 | 注釋 |
Constant Coefficient & Constant Term
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yc﹕
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yp﹕
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Stability |
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Non-oscillatory | h > 0 |
Oscillatory | h < 0 |
Divergent | | h | > 1 |
Convergent | | h | < 1 | |
[ h = - α ] |
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Second-Order Linear Difference Equations
名稱 | 樣式 | 注釋 |
Constant Coefficient & Constant Term
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yp﹕
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yc﹕
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1 ) Distinct Real Roots: |
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2 ) Repeated Real Roots: |
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3 ) Complex Roots:
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Stability |
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1 ) Distinct Real Roots: |
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2 ) Repeated Real Roots: |
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3 ) Complex Roots: |
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