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#1 2014-05-02 00:41:02
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Modified Euler method
Use modified Euler method with (h=0.1) to solve the following differential equation:
d2y/dx2=2+y/x , Where y(1)=1 for x=1 to 1.4
How to convert second derivative to first derivative
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#2 2014-05-02 01:03:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Hi ammar;
The Euler method ( modified or not ) is usually for a first order ODE.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2014-05-02 01:10:10
- ammar
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- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
Yes,but we can solve it by change the second derivative to first derivative but how to change this equation ?
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#4 2014-05-02 01:13:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Yes, you can change any second order de into 2 first order or coupled ones.
I have to get offline for a bit, in the meantime watch this video. When I get back if it still is a problem then we will work on it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2014-05-02 01:26:51
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
my problem is : can I assume dy/dx=z when this equation does not contain dy/dx
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#6 2014-05-02 04:36:20
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Hi;
Is the first equation, the second is
You left out an initial condition in your original problem.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2014-05-02 04:42:51
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
OK that's what I need to know
Thanks for help 
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#8 2014-05-02 04:43:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
What is the missing initial condition?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2014-05-02 05:11:51
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
y0=1
x0=1
do you mean ?
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#10 2014-05-02 05:18:49
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
There should be a y'(x) too. But just to get the 2 equations you do not need it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#11 2014-05-02 05:38:21
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
The equation doesn't have (dy/dx) ,I think I don't need it
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#12 2014-05-02 06:15:07
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
Can I make Integral to converted to first derivative ?
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#13 2014-05-02 08:27:33
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Can I make Integral to converted to first derivative ?
I am not following you. What do you mean?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2014-05-02 16:27:50
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
convert (d2y/dx2=2+y/x) to (dy/dx) by integral ??
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#15 2014-05-02 19:53:53
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Hi;
Can you copy the question exactly as it appears?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2014-05-02 22:07:30
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
∫d2y/dx2=∫(2+y/x)
this lead to
dy/dx=2x+y*ln(x) , is this correct ?
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#17 2014-05-02 22:11:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Oh I see what you wanted now. Sorry, I did not understand. Yes, that is what I would get.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2014-05-02 22:17:03
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
But I think it's would be dy/dx=2x+y*ln(x)+constant
and if we have a boundary condition (dy/dx) I will find the constant
but in the question the boundary is y(1)=1, that's not work
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#19 2014-05-02 22:18:23
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Yes, there would be a constant.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#20 2014-05-02 22:25:50
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
OK that's mean the integral to find the first derivative does't work
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#21 2014-05-02 22:29:19
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
That is why I asked you what the initial conditions were. You need 2, y(1) = 1 and y'(x) = something.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#22 2014-05-02 23:11:28
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
OK thanks for help I'll try to solve it by the assumption of dy/dx=z
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#23 2014-05-03 01:08:33
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
Usually then you need z(0).
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#24 2014-05-03 05:25:07
- ammar
- Member
- Registered: 2013-12-16
- Posts: 69
Re: Modified Euler method
Yes but the question like i posted , any idea for solving ?
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#25 2014-05-03 07:21:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modified Euler method
How can you determine the constant without another initial condition?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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