How to solve differential equations?

[johanpg]

Hello,

I am new with differential equations, and need to know how to solve a simple one:

EI*y''(x) = M(x)

M(x) = w*x/2

Initial conditions:

x=0, y(0) = 0

x= L/2 y'(L/2) = 0

Thank you,
Johan

[ValeryOchkov]

Numericaly:


Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[ptc-1368288]

On 1/9/2010 3:57:40 PM, johanpg wrote:
>Hello,
>
>I am new with differential
>equations, and need to know
>how to solve a simple one:
>
>EI*y''(x) = M(x)
>
>M(x) = w*x/2
>
>Initial conditions:
>
>x=0, y(0) = 0
>
>x= L/2 y'(L/2) = 0
>
>Thank you,
>Johan
________________________

For that one, just go by Valery solution.
If you are new to DE, and want to get in it seriously, one of the best book is:

Mathematics of Physics and Modern Engineering
I.S. SOKOLNIKOFF & R.M. REDHEFFER

I'm using the 2nd edition (1966).
Whatever Mathcad can or will do for you, must be founded. You could also purchase the Valery book about DE and Mathcad (Springer Verlag).

jmG

[johanpg]

Hello,

Thank you very much for your answers. I'm tryng to use the Odesolve, and I have an error (the command is in red) and a message telling me:

No "Given" found to open this solve block.

I also would like to know how to solve this simple symbolic equation not using numbers. I am using MathCad 14.

Thank you,
Johan

[RichardJ]

On 1/11/2010 10:06:15 AM, johanpg wrote:
>Hello,
>
>Thank you very much for your
>answers. I'm tryng to use the
>Odesolve, and I have an error
>(the command is in red) and a
>message telling me:
>
>No "Given" found to open this
>solve block.

The error is exactly what it says. After the assignments of EI, L and w type the keyword "Given". Perhaps you should look up solve blocks in the help.

>I also would like to know how
>to solve this simple symbolic
>equation not using numbers. I
>am using MathCad 14.

Mathcad does not do symbolic solutions of ODEs.

Richard

[AlvaroDíaz]

See attached.

Regards. Alvaro.

[johanpg]

Thank you Alvaro, your answer is what I was looking for

Muchas gracias!!!

Johan

[johanpg]

Hello Alvaro,

Now I am dealing with the Galerkin Method.

I need to manipulate a 4 order differential equation to introduce (2) natural boundary conditions and obtain a low order differential equation.

I need help in How can I manipulate the 4 order differential equation to obtain a low order diferential equation.

See attached file.

Thank you,
Johan

[ptc-1368288]

On 1/16/2010 2:28:14 PM, johanpg wrote:
>Hello Alvaro,
>
>Now I am dealing with the
>Galerkin Method.
>
>I need to manipulate a 4 order
>differential equation to
>introduce (2) natural boundary
>conditions and obtain a low
>order differential equation.
>
>I need help in How can I
>manipulate the 4 order
>differential equation to
>obtain a low order differential
>equation.
>
>See attached file.
>
>Thank you,
>Johan
_________________________

For "lower order", that's how RK works.
For your work sheet, the result from the first integration, you could collocate into a Cheby polynomial. As well as for the 2nd integrator. The idea of collocation is a polynomial result formula, that enables export to low level software. By inspection, your procedure looks OK.

jmG

[ptc-1368288]

... back to Galerkin, here is a work sheet in finite differences.

jmG

[PhilipOakley]

Also don't forget the Wavelet Galerkin methods as an
option - a variation of multi-grid.

It's an area I need to be interested in but haven't
got there yet (still at the collating phase 😉

Philip Oakley

[ptc-1368288]

On 1/11/2010 11:06:34 AM, rijackson wrote:
...
>Mathcad does not do symbolic solutions of ODEs.
>
>Richard
_____________________

Mathcad 11.2a does all the symbolic I have published.
Do you mean 14 does not understand my Laplace solvers ?

jmG

[RichardJ]

I meant what I said. I did not say it could not be done in Mathcad, in at least some cases, if you know what to do and lead it through all the steps. I said Mathcad couldn't do it.

Richard

[ptc-1368288]

On 1/12/2010 3:59:30 PM, rijackson wrote:
>I meant what I said. I did not
>say it could not be done in
>Mathcad, in at least some
>cases, if you know what to do
>and lead it through all the
>steps. I said Mathcad couldn't
>do it.
>
>Richard
_______________________________

A pity if Mathcad 14 does not run this work sheet.
We have lot more symbolic DE solvers that these two.

jmG