Mixing
Solution to differential equation by Runge-Kutta
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Given $Y' = Y^2 - X^2$ where $Y(0)=2$. Find $Y(0.1)$ and $Y(0.2)$ by second order Runge-Kutta.
Here is my workings.
$$
h=0.1, quad x(0)=0,quad Y(0)=2\
f(x,y) = Y^2 - X^2\
k_1 = hf(x,y) = 0.1(2^2-0^2) = 0.4000\
beginalignk_2&= hf(x+h, y+h) \&= 0.1+(0+0.01, 2+0.4000)
\&= 0.1(2.4^2-0.1^2) = 0.5750endalign\
Y_1= y+frac12[k_1+k_1]
= 2+ frac12[0.4000+0.5750] = 2.4875.
$$
How can i get the $Y_2$?
analysis
edited Aug 6 at 11:49
Arthur
99k793175
asked Aug 6 at 11:42
Adeshina
6
add a comment |Â
up vote
-2
down vote
favorite
Given $Y' = Y^2 - X^2$ where $Y(0)=2$. Find $Y(0.1)$ and $Y(0.2)$ by second order Runge-Kutta.
Here is my workings.
$$
h=0.1, quad x(0)=0,quad Y(0)=2\
f(x,y) = Y^2 - X^2\
k_1 = hf(x,y) = 0.1(2^2-0^2) = 0.4000\
beginalignk_2&= hf(x+h, y+h) \&= 0.1+(0+0.01, 2+0.4000)
\&= 0.1(2.4^2-0.1^2) = 0.5750endalign\
Y_1= y+frac12[k_1+k_1]
= 2+ frac12[0.4000+0.5750] = 2.4875.
$$
How can i get the $Y_2$?
analysis
edited Aug 6 at 11:49
Arthur
99k793175
asked Aug 6 at 11:42
Adeshina
6
I have edited your post to format the math correctly, using MathJax. It isn't perfect, but it's a lot more readable. If you press the "edit" button at the bottom of your question post, you can see how I did it. Please look through what I've written and check that it is correct. Also, consider using MathJax yourself in the future to help the readability of your questions.
– Arthur
Aug 6 at 11:54
Thanks bro. New here, i dont know how to type that with my mobile.
– Adeshina
Aug 6 at 12:00
No worries. I do it on the mobile all the time (too often, some might say). It takes some practice, and I think I'm pretty decent at it, but it will never beat computer typing.
– Arthur
Aug 6 at 12:01
I will like to learn that. Whats the name of the keypad app you using?
– Adeshina
Aug 6 at 12:06
I just use the standard keboard that came on my phone. It's clunky, but it's what I have. The dollar sign, backslash and curly brackets are hidden away somewhat, but I barely notice that any more.
– Arthur
Aug 6 at 12:15
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Given $Y' = Y^2 - X^2$ where $Y(0)=2$. Find $Y(0.1)$ and $Y(0.2)$ by second order Runge-Kutta.
Here is my workings.
$$
h=0.1, quad x(0)=0,quad Y(0)=2\
f(x,y) = Y^2 - X^2\
k_1 = hf(x,y) = 0.1(2^2-0^2) = 0.4000\
beginalignk_2&= hf(x+h, y+h) \&= 0.1+(0+0.01, 2+0.4000)
\&= 0.1(2.4^2-0.1^2) = 0.5750endalign\
Y_1= y+frac12[k_1+k_1]
= 2+ frac12[0.4000+0.5750] = 2.4875.
$$
How can i get the $Y_2$?
analysis
edited Aug 6 at 11:49
Arthur
99k793175
asked Aug 6 at 11:42
Adeshina
6
Given $Y' = Y^2 - X^2$ where $Y(0)=2$. Find $Y(0.1)$ and $Y(0.2)$ by second order Runge-Kutta.
Here is my workings.
$$
h=0.1, quad x(0)=0,quad Y(0)=2\
f(x,y) = Y^2 - X^2\
k_1 = hf(x,y) = 0.1(2^2-0^2) = 0.4000\
beginalignk_2&= hf(x+h, y+h) \&= 0.1+(0+0.01, 2+0.4000)
\&= 0.1(2.4^2-0.1^2) = 0.5750endalign\
Y_1= y+frac12[k_1+k_1]
= 2+ frac12[0.4000+0.5750] = 2.4875.
$$
How can i get the $Y_2$?
analysis
edited Aug 6 at 11:49
Arthur
99k793175
asked Aug 6 at 11:42
Adeshina
6
edited Aug 6 at 11:49
Arthur
99k793175
edited Aug 6 at 11:49
Arthur
99k793175
edited Aug 6 at 11:49
Arthur
99k793175
99k793175
asked Aug 6 at 11:42
Adeshina
6
asked Aug 6 at 11:42
Adeshina
6
asked Aug 6 at 11:42
Adeshina
6
6
I have edited your post to format the math correctly, using MathJax. It isn't perfect, but it's a lot more readable. If you press the "edit" button at the bottom of your question post, you can see how I did it. Please look through what I've written and check that it is correct. Also, consider using MathJax yourself in the future to help the readability of your questions.
– Arthur
Aug 6 at 11:54
Thanks bro. New here, i dont know how to type that with my mobile.
– Adeshina
Aug 6 at 12:00
No worries. I do it on the mobile all the time (too often, some might say). It takes some practice, and I think I'm pretty decent at it, but it will never beat computer typing.
– Arthur
Aug 6 at 12:01
I will like to learn that. Whats the name of the keypad app you using?
– Adeshina
Aug 6 at 12:06
I just use the standard keboard that came on my phone. It's clunky, but it's what I have. The dollar sign, backslash and curly brackets are hidden away somewhat, but I barely notice that any more.
– Arthur
Aug 6 at 12:15
add a comment |Â
I have edited your post to format the math correctly, using MathJax. It isn't perfect, but it's a lot more readable. If you press the "edit" button at the bottom of your question post, you can see how I did it. Please look through what I've written and check that it is correct. Also, consider using MathJax yourself in the future to help the readability of your questions.
– Arthur
Aug 6 at 11:54
Thanks bro. New here, i dont know how to type that with my mobile.
– Adeshina
Aug 6 at 12:00
No worries. I do it on the mobile all the time (too often, some might say). It takes some practice, and I think I'm pretty decent at it, but it will never beat computer typing.
– Arthur
Aug 6 at 12:01
I will like to learn that. Whats the name of the keypad app you using?
– Adeshina
Aug 6 at 12:06
I just use the standard keboard that came on my phone. It's clunky, but it's what I have. The dollar sign, backslash and curly brackets are hidden away somewhat, but I barely notice that any more.
– Arthur
Aug 6 at 12:15
I have edited your post to format the math correctly, using MathJax. It isn't perfect, but it's a lot more readable. If you press the "edit" button at the bottom of your question post, you can see how I did it. Please look through what I've written and check that it is correct. Also, consider using MathJax yourself in the future to help the readability of your questions.
– Arthur
Aug 6 at 11:54
I have edited your post to format the math correctly, using MathJax. It isn't perfect, but it's a lot more readable. If you press the "edit" button at the bottom of your question post, you can see how I did it. Please look through what I've written and check that it is correct. Also, consider using MathJax yourself in the future to help the readability of your questions.
– Arthur
Aug 6 at 11:54
Thanks bro. New here, i dont know how to type that with my mobile.
– Adeshina
Aug 6 at 12:00
Thanks bro. New here, i dont know how to type that with my mobile.
– Adeshina
Aug 6 at 12:00
No worries. I do it on the mobile all the time (too often, some might say). It takes some practice, and I think I'm pretty decent at it, but it will never beat computer typing.
– Arthur
Aug 6 at 12:01
No worries. I do it on the mobile all the time (too often, some might say). It takes some practice, and I think I'm pretty decent at it, but it will never beat computer typing.
– Arthur
Aug 6 at 12:01
I will like to learn that. Whats the name of the keypad app you using?
– Adeshina
Aug 6 at 12:06
I will like to learn that. Whats the name of the keypad app you using?
– Adeshina
Aug 6 at 12:06
I just use the standard keboard that came on my phone. It's clunky, but it's what I have. The dollar sign, backslash and curly brackets are hidden away somewhat, but I barely notice that any more.
– Arthur
Aug 6 at 12:15
I just use the standard keboard that came on my phone. It's clunky, but it's what I have. The dollar sign, backslash and curly brackets are hidden away somewhat, but I barely notice that any more.
– Arthur
Aug 6 at 12:15
add a comment |Â
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I have edited your post to format the math correctly, using MathJax. It isn't perfect, but it's a lot more readable. If you press the "edit" button at the bottom of your question post, you can see how I did it. Please look through what I've written and check that it is correct. Also, consider using MathJax yourself in the future to help the readability of your questions.
– Arthur
Aug 6 at 11:54
Thanks bro. New here, i dont know how to type that with my mobile.
– Adeshina
Aug 6 at 12:00
No worries. I do it on the mobile all the time (too often, some might say). It takes some practice, and I think I'm pretty decent at it, but it will never beat computer typing.
– Arthur
Aug 6 at 12:01
I will like to learn that. Whats the name of the keypad app you using?
– Adeshina
Aug 6 at 12:06
I just use the standard keboard that came on my phone. It's clunky, but it's what I have. The dollar sign, backslash and curly brackets are hidden away somewhat, but I barely notice that any more.
– Arthur
Aug 6 at 12:15