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Answer this question or recommend an answer
Numerical Solution
an+1 = 0.8an - 100, a0 = 500
Build a numerical solution for the following initial-value problems. Plot your data to observe patterns in the solution. Is there an equilibrium solution? Is it stable or unstable.
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- By Sharon |
- Category: other - mathematics |
- Grade level: college and above
- Aug/27/2008 |
- Answers to this question: 1
|
Answer by: Ganesha
First Answer Best Answer| an+1 | an | 100 | (0.8)(an)-100 |
| a1 | 400 | 100 | 300 |
| a2 | 240 | 100 | 140 |
| a3 | 112 | 101 | 12 |
| a4 | 9.6 | 102 | -90.4 |
| a5 | -72.32 | 103 | -172.32 |
| a6 | -137.856 | 104 | -237.856 |
| a7 | -190.2848 | 105 | -290.2848 |
| a8 | -232.22784 | 106 | -332.22784 |
| a9 | -265.782272 | 107 | -365.782272 |
| a10 | -292.6258176 | 108 | -392.6258176 |
| a11 | -314.1006541 | 109 | -414.1006541 |
| a12 | -331.2805233 | 110 | -431.2805233 |
| a13 | -345.0244186 | 111 | -445.0244186 |
| a14 | -356.0195349 | 112 | -456.0195349 |
| a15 | -364.8156279 | 113 | -464.8156279 |
| a16 | -371.8525023 | 114 | -471.8525023 |
| a17 | -377.4820019 | 115 | -477.4820019 |
| a18 | -381.9856015 | 116 | -481.9856015 |
| a19 | -385.5884812 | 117 | -485.5884812 |
| a20 | -388.470785 | 118 | -488.470785 |
| a21 | -390.776628 | 119 | -490.776628 |
| a22 | -392.6213024 | 120 | -492.6213024 |
| a23 | -394.0970419 | 121 | -494.0970419 |
| a24 | -395.2776335 | 122 | -495.2776335 |
| a25 | -396.2221068 | 123 | -496.2221068 |
| a26 | -396.9776855 | 124 | -496.9776855 |
| a27 | -397.5821484 | 125 | -497.5821484 |
| a28 | -398.0657187 | 126 | -498.0657187 |
| a29 | -398.452575 | 127 | -498.452575 |
| a30 | -398.76206 | 128 | -498.76206 |
| a31 | -399.009648 | 129 | -499.009648 |
| a32 | -399.2077184 | 130 | -499.2077184 |
| a33 | -399.3661747 | 131 | -499.3661747 |
| a34 | -399.4929398 | 132 | -499.4929398 |
| a35 | -399.5943518 | 133 | -499.5943518 |
| a36 | -399.6754814 | 134 | -499.6754814 |
| a37 | -399.7403852 | 135 | -499.7403852 |
| a38 | -399.7923081 | 136 | -499.7923081 |
| a39 | -399.8338465 | 137 | -499.8338465 |
| a40 | -399.8670772 | 138 | -499.8670772 |
| a41 | -399.8936618 | 139 | -499.8936618 |
| a42 | -399.9149294 | 140 | -499.9149294 |
| a43 | -399.9319435 | 141 | -499.9319435 |
| a44 | -399.9455548 | 142 | -499.9455548 |
| a45 | -399.9564439 | 143 | -499.9564439 |
| a46 | -399.9651551 | 144 | -499.9651551 |
| a47 | -399.9721241 | 145 | -499.9721241 |
| a48 | -399.9776993 | 146 | -499.9776993 |
| a49 | -399.9821594 | 147 | -499.9821594 |
| a50 | -399.9857275 | 148 | -499.9857275 |
a0 = 500.
a1 = 0.8a0-1= 0.8*500-100=400-100=300.
a2=0.8(a1)-100=0.8*300-100=240-100=140'
See the table for a3 and onward.l
You can see the generated values of an , written like an. See that the value of a4 becomes negative. Also you can see that value approaches -500 for large n and is going stable .
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- Aug/30/2008 |
- Answers by Ganesha: 1193 |
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