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#### Solving a differential equation numerically in Mathematica

```Hi all,

Does anyone know if Mathematica can numerically solve a second order differential equation?

``` 0 4/27/2007 9:32:38 AM comp.soft-sys.math.mathematica  28821 articles. 0 followers. 8 Replies 700 Views Similar Articles

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```Blake Jackson wrote:
> Hi all,
>
> Does anyone know if Mathematica can numerically solve a second order differential equation?
>

Sure it can. Search the documentation for *NDSolve* . For example
(adapted from , which is a nice and short introduction to solving
ODEs with Mathematica),

In:=
sol = NDSolve[
{Derivative[x][t] + gamma*Derivative[x][t] +
x[t]^3 == A*Cos[t], x == 0.6,
Derivative[x] == 1.25} /.
{gamma -> 0.15, A -> 0.3}, x, {t, 0, 100}]
Plot[x[t] /. sol, {t, 0, 100}]

Out=
{{x -> InterpolatingFunction[]}}

Out=
Graphics[]

Regards,
Jean-Marc

 _Mathematica 5.2 Documentation_, "Built-in Functions / Numerical
Computation / Equation Solving / NDSolve",
http://documents.wolfram.com/mathematica/functions/NDSolve

 _Integrating Equations of Motion in Mathematica_, Gary L. Gray,
Assistant Professor, Engineering Science and Mechanics, The Pennsylvania
State University,
http://www.esm.psu.edu/courses/emch12/IntDyn/course-docs/Mathematica/MmaGuide-GLG.pdf

``` 0 4/28/2007 9:53:06 AM
```Blake Jackson wrote:
> Hi all,
>
> Does anyone know if Mathematica can numerically solve a second order differential equation?
>

http://documents.wolfram.com/mathematica/functions/NDSolve

``` 0 4/28/2007 9:54:07 AM
```
Hi,

it depends on the differential equation (DE). For most DE that occur in

hope this helps, Daniel

Blake Jackson wrote:

> Hi all,

>

> Does anyone know if Mathematica can numerically solve a second order differential equation?

>

``` 0 4/28/2007 10:03:29 AM
```Hi,

yes.

Regards
Jens

Blake Jackson wrote:
> Hi all,
>
> Does anyone know if Mathematica can numerically solve a second order differential equation?
>

``` 0 4/28/2007 10:13:42 AM
```Of course! See the documentation on "NDSolve" or evaluate "?NDSolve"
to avoid searching

=CF/=C7 Blake Jackson =DD=E3=F1=E1=F8=E5:
> Hi all,
>
> Does anyone know if Mathematica can numerically solve a second order diff=
erential equation?

``` 0 4/28/2007 10:14:43 AM
```..=2E.in praxis...

Hi David.
Did you know that praxis is a greek word?

http://en.wikipedia.org/wiki/Praxis_%28word%29

Cheers
Dimitris

=CF/=C7 dh =DD=E3=F1=E1=F8=E5:
> Hi,
>
> it depends on the differential equation (DE). For most DE that occur in
>
>
> hope this helps, Daniel
>
>
>
> Blake Jackson wrote:
>
> > Hi all,
>
> >
>
> > Does anyone know if Mathematica can numerically solve a second order di=
fferential equation?
>
> >

``` 0 4/29/2007 7:10:01 AM
```If you are interested to more greek words encountered in english
vocabulary see here...

http://en.wikipedia.org/wiki/Xenophon_Zolotas

about a Greek economist which is...also famous for demonstrating the
contribution of Greek language to the English vocabulary by making
English speeches, as he said, "using with the exception of articles
and prepositions only Greek words", to foreign audiences.

Dimitris

=CF/=C7 dh =DD=E3=F1=E1=F8=E5:
> Hi,
>
> it depends on the differential equation (DE). For most DE that occur in
>
>
> hope this helps, Daniel
>
>
>
> Blake Jackson wrote:
>
> > Hi all,
>
> >
>
> > Does anyone know if Mathematica can numerically solve a second order di=
fferential equation?
>
> >

``` 0 4/29/2007 7:15:06 AM
```Blake Jackson wrote:
> Hi all,
>
> Does anyone know if Mathematica can numerically solve a second order differential equation?
>
This is a bit like asking if it is possible to hire a car when visiting
the US!

David Bailey
http://www.dbaileyconsultancy.co.uk

``` 0 4/30/2007 7:41:30 AM