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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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-05-02 01:10:10

ammar
Member
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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.

http://www.youtube.com/watch?v=k2V2UYr6lYw


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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  smile   smile   smile

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#8 2014-05-02 04:43:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

Re: Modified Euler method

What is the missing initial condition?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

Re: Modified Euler method

Yes, there would be a constant.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

Re: Modified Euler method

Usually then you need z(0).


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,188

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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