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Use Euler's method with step size0.4 to estimatey(2) , where y(x) is the solution of the initial-value problem y'=4x+y^2, y(0)=...Asked by Geminese
Use euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem
y'= -3x+y^2, y(0)=1
y'= -3x+y^2, y(0)=1
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Answered by
Steve
what's the problem? Just plug and chug:
Y<sub>i+1</sub> = y<sub>i</sub> + .2*y'(x<sub>i</sub>,y<sub>i</sub>)
0: (0.0000,1.0000) -> 1.2000
1: (0.2000,1.2000) -> 1.3680
2: (0.4000,1.3680) -> 1.5023
3: (0.6000,1.5023) -> 1.5937
4: (0.8000,1.5937) -> 1.6216
5: (1.0000,1.6216) -> 1.5475
Looks like f(1) = 1.6216
Y<sub>i+1</sub> = y<sub>i</sub> + .2*y'(x<sub>i</sub>,y<sub>i</sub>)
0: (0.0000,1.0000) -> 1.2000
1: (0.2000,1.2000) -> 1.3680
2: (0.4000,1.3680) -> 1.5023
3: (0.6000,1.5023) -> 1.5937
4: (0.8000,1.5937) -> 1.6216
5: (1.0000,1.6216) -> 1.5475
Looks like f(1) = 1.6216
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