Лабораторные работы / Отчеты / Метод Эйлера - Павлов - 2006 / Павло
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2,718 |
<x< |
3,7182 |
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Павлов В. Вариант 15 Ф-22 |
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Метод Эйлера |
n= |
5 |
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i |
xi |
yi |
f(xi,yi) |
y(i+1) |
yi теор |
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xi |
yi |
f(xi,yi) |
y((i+1)/2) |
f(xi+1/2,yi+1/2) |
yi+1 |
Yi тeор |
0 |
2,718 |
0 |
1 |
0,2 |
-8E-05 |
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2,718 |
0 |
1 |
0,1 |
1,0006 |
0,2001 |
-8E-05 |
1 |
2,918 |
0,2 |
1,0023 |
0,4005 |
0,2001 |
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2,918 |
0,2001 |
1,0023 |
0,3004 |
1,0048 |
0,4011 |
0,2001 |
2 |
3,118 |
0,4005 |
1,0077 |
0,602 |
0,4011 |
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3,118 |
0,4011 |
1,0079 |
0,5019 |
1,0115 |
0,6034 |
0,4011 |
3 |
3,318 |
0,602 |
1,0152 |
0,805 |
0,6034 |
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3,318 |
0,6034 |
1,0156 |
0,7049 |
1,0198 |
0,8074 |
0,6034 |
4 |
3,518 |
0,805 |
1,0238 |
1,0098 |
0,8074 |
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3,518 |
0,8074 |
1,0244 |
0,9098 |
1,0291 |
1,0132 |
0,8074 |
5 |
3,718 |
1,0098 |
1,0331 |
1,2164 |
1,0132 |
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3,718 |
1,0132 |
1,034 |
1,1166 |
1,0388 |
1,2209 |
1,0132 |
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Модифицированный метод эйлера |
n= |
10 |
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i |
xi |
yi |
f(xi,yi) |
-0,253 |
0,1687 |
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xi |
yi |
f(xi,yi) |
y((i+)/2 |
f(xi+1/2,yi+1/2) |
yi+1 |
yi теор |
0 |
2,718 |
0 |
1 |
0,1 |
-8E-05 |
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2,718 |
0 |
1 |
0,05 |
1,0002 |
0,1 |
-8E-05 |
1 |
2,818 |
0,1 |
1,0006 |
0,2001 |
0,0999 |
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2,818 |
0,1 |
1,0006 |
0,1501 |
1,0014 |
0,2002 |
0,0999 |
2 |
2,918 |
0,2001 |
1,0023 |
0,3003 |
0,2001 |
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2,918 |
0,2002 |
1,0023 |
0,2503 |
1,0035 |
0,3005 |
0,2001 |
3 |
3,018 |
0,3003 |
1,0048 |
0,4008 |
0,3004 |
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3,018 |
0,3005 |
1,0048 |
0,3507 |
1,0063 |
0,4011 |
0,3004 |
4 |
3,118 |
0,4008 |
1,0078 |
0,5016 |
0,4011 |
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3,118 |
0,4011 |
1,008 |
0,4515 |
1,0097 |
0,5021 |
0,4011 |
5 |
3,218 |
0,5016 |
1,0114 |
0,6027 |
0,502 |
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3,218 |
0,5021 |
1,0116 |
0,5527 |
1,0135 |
0,6035 |
0,502 |
6 |
3,318 |
0,6027 |
1,0154 |
0,7042 |
0,6034 |
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3,318 |
0,6035 |
1,0156 |
0,6542 |
1,0177 |
0,7052 |
0,6034 |
7 |
3,418 |
0,7042 |
1,0196 |
0,8062 |
0,7052 |
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3,418 |
0,7052 |
1,0199 |
0,7562 |
1,0221 |
0,8074 |
0,7052 |
8 |
3,518 |
0,8062 |
1,0241 |
0,9086 |
0,8074 |
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3,518 |
0,8074 |
1,0244 |
0,8587 |
1,0268 |
0,9101 |
0,8074 |
9 |
3,618 |
0,9086 |
1,0287 |
1,0115 |
0,91 |
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3,618 |
0,9101 |
1,0292 |
0,9616 |
1,0315 |
1,0133 |
0,91 |
10 |
3,718 |
1,0115 |
1,0335 |
1,1148 |
1,0132 |
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3,718 |
1,0133 |
1,034 |
1,065 |
1,0364 |
1,1169 |
1,0132 |