Solving nonlinear coupled differential equations in Mathematica 7.0Here is a set of equations I would like to solve
y''[x]==y+z'[x]
z[x]^3=y'[x]+3
With boundary conditions of y[1]==2 and y[0]==3
Using NDSolve on these equations, Mathematica says the order of the
equations is 3 and it has only 2 initial conditions. But the order of
this system of equations is 2 as far as I see (since order is defined
as the highest derivative)
When I do try to put another boundary condition in like z[0]==0
Mathematica spits out that it cant solve for the derivatives and is
using a mass matrix method (error:ntdvmm) and then it says that it has
...
Re: Mathematica hangs when solving sys. of equations w/certain parametersMr Lichtblau:
Thank you very much for the detailed response. I really appreciate your
help. I'm on a tight deadline and am really swamped with other work at
the moment, but I'll read what you wrote and get back to you.
Regards,
Sean
On Wed, 30 Mar 2005, Daniel Lichtblau wrote:
> Sean wrote:
> > I am trying to find local maxima of an objective function by solving the FOCs of a function of 4 control variables (pL,pH,phiL,phiH) and 3 parameters (c, pDBS,phiDBS).
> >
> > The objective function is
> >
> > f[pL_,phiL_,pH_,phiH_,pDBS_,phiDBS_,c_] = \
> > (pL-0.5c*phiL^2)*((pH-pL)/(phiH-phiL) - pL/phiL) + \
> > (pH-0.5c*phiH^2)*((pDBS-pH)/(phiDBS-phiH) - (pH-pL)/(phiH-phiL))
> >
> > I find the FOCs by differentiating with respect to each of the 4 control variables, and then I solve the system using Solve[] (see details below)
> >
> > For certain values of the parameters (c, pDBS, phiDBS), the Solve[] routine works fine. But I can't figure out why Solve[] just seems to hang for other parameter values. I have verified that it's not because I'm dividing by zero or anything, and the points that are causing problems seem to be totally generic.
> >
> > For example, everything works fine when (c=0.1, pDBS=5, phiDBS=8) and when (c=0.1, pDBS=7, phiDBS=8), but not when (c=0.1, pDBS=6, phiDBS=8). I happen to know that at these latter parameter values, one of the s...
Re: Help to solve an integral by using Mathematica Integrate[Sqrt[tTo my surprise, Mathematica has been very reluctant to help here, despite
the
seemingly simple form of the integral. Here is what I did anyway:
1. Find an indefinite integral:
In[94]:= expr = Integrate[Sqrt[t (1 - t) (z - t)], t]
Out[94]= (Sqrt[(-1 + t) t (t - z)] (2 t (-1 + 3 t - z) + (
2 (-1 + t) (-((2 t (t - z) (1 - z + z^2))/(-1 + t)^2) - (
2 I Sqrt[t/(-1 + t)] Sqrt[(
t - z)/(-1 + t)] (1 - z + z^2) EllipticE[
I ArcSinh[1/Sqrt[-1 + t]], 1 - z])/Sqrt[-1 + t] + (
I Sqrt[t/(-1 + t)] Sqrt[(t - z)/(-1 + t)]
z (1 + z) EllipticF[I ArcSinh[1/Sq...
system of nonlinear equations in mathematica?Hai all,
I am tryign to solve a system of nonlinear differential equations using mathematica.I think there exists singularity in my equations and am new to mathematica and donoy know i to get the problem resolved.Please help me out in this.thought to attach my equations here which i couldnt do.please do reply me through email to saihone@gmail.com.
0.5(derivative(f)+x(derivative(derivative(x))= - derivative(0.1*k^2/d(derivative(derivative(f))));
-10(k+0.5*x*derivative(k)) = derivative(0.1*k*k*derivative(k)/d) + 0.1*k^2*(derivative(derivative(f))^2/d - d;
10(-2d-derivative(d)*x/2) =...
Solving finite field equations in MathematicaHi,
I would need to solve a system of finite field (GF(2)) equations
with mathematica. I have looked around, and the only thing I can find
is a 1993 ``finite field package''. What is the simplest way with
current versions of mathematica?
Thanks,
Emanuele
...
How can I solve these equations using mathematica?HI,members
I have a equation group as fellowed:
(x1-x10)^2 + (y1-y10)^2= = a
..........................................1
(x2-x20)^2 + (y2-y20)^2 = = b
...........................................2
(x3-x30)^2+ (y3-y30)^2 = = c
.................................................3
(x1-x2)^2+(y1-y2)^2 = = d1
....................................................4
(x1-x3)^2+(y1-y3)^2 = = d2
.......................................................5
(x3-x2)^2+(y3-y2)^2 = = d3
............................................................6
where x1,y1,x2,y2,x3,y3 are an unknown quantities,...
Solve a couple mode equation with Mathematica.To whom my concern,
w = 2 *\[Pi]*f;
c = 3*10^8;
nnl = 0.01;
L = 3000*10^-6;
eqns1 = A1'[z] == -(w/c)*(2*nnl)/\[Pi]*((Abs[A1 (z)])^2 + (Abs[A2 (z)])
^2)*A2[z];
eqns2 = A2'[z] == -(w/c)*(2*nnl)/\[Pi]*((Abs[A1 (z)])^2 + (Abs[A2 (z)])
^2)*A1[z];
eqns3 = A1[0] == 1;
eqns4 = A2[L] == 0;
DSolve[{eqns1, eqns2, eqns3, eqns4}, {A1[z], A2[z]}, z]
I am trying solve A1[z] and A2[z] in terms of f.
Any help will be appreciated.
Thanks.
Some function brackets you use are '( )' instead of the required '[ ]'
Cheers -- Sjoerd
On May 18, 12:17 pm, jty...@p...
How to solve stochastic differential equations in Mathematica?Could you please show me some simple examples ? Thank you very much.
In article <ds9n49$69$1@smc.vnet.net>,
"Jackie" <Shuangshuang.Zhou@gmail.com> wrote:
> Could you please show me some simple examples ? Thank you very much.
See
http://library.wolfram.com/infocenter/MathSource/1170/
tovsn3: Doing Stochastic Calculus with Mathematica
http://library.wolfram.com/infocenter/Books/3375
http://library.wolfram.com/infocenter/Conferences/3959/
Cheers,
Paul
_______________________________________________________________________
Paul Abbo...
Problems with solving integrals in Mathematica 9Has anybody encountered the same problems with solving integrals in Ver. 9 as I did?
Here a very simple example:
Integrate[D[f[x], x] / f[x], {x, 0, T}]
Version 8.04 gives the correct results:
-Log[f[0]] + Log[f[T]]
In Version 9.00 as well as 9.01 this integral can't be solved. With more complicated integrals I had the same problems. Version 8 gives a solution, Version 9 doesn't!
Could some other Version 9 users try it.
On 6/1/2013 3:06 AM, Jost Adler wrote:
> Has anybody encountered the same problems with solving integrals in Ver. 9 as I did?
>
> Here a very simple example:
>
> Integrate[D[f[x], x] / f[x], {x, 0, T}]
>
....
In case the previous explanations are too obscure, may I point out that
it is the [second?] fundamental theorem of the integral calculus (FTIC)
which allows one to compute the
integral of f'(x) with respect to x, from A to B
by computing f(B)-f(A).
FTIC requires some constraints on f. Read your favorite calculus text
to learn more. (Depending on the sophistication of your text, you may
see various formulations of these constraints.)
So Mathematica is doing the right thing in version 9 in this situation,
I think.
...
Can Mathematica solve this differential equation ?In beam bending, we have the following situation:
y '' [x] = M(x), boundary conditions specified for y[0] and y[1]
Simple enough, but the problem arises as M is a piecewise-defined
function (linear in all pieces though)
i.e., M(x) = M1(x) for 0<x<1
and M(x) = M2(x) for 1<x<2
M(x) = 0 for all other values of x
Obviously, we are only interested in the interval 0<x<1
This leads to two separate equations:
y1'' [x] = M1(x) in 0<x<1
y2 '' [x] = M2(x) in 1 <x <2
Now we will have 4 constants of integration. We therefore...
solve partial differential equations with mathematicaHello,
I'd like to solve the following partial differential equation with
Mathematica,
eqn = D[u[r, t], t] == d D[u[r, t], r, r] - k u[r, t]/r
by doing:
DSolve[{eqn, u[r, 0] == 0, u[0.000000001, t] == ui, u[\[Infinity], t]
== 0}, u[r, t], {r, t}]
d,k and ui are constants.
In DSolve i include also the boundary conditions but I am still not
able to solve it.
Do you have any suggestions for solving the problem?
Thanks very much for your help.
Dino.
The PDEs that DSolve can solve are still mostly single first-order
equations. Other than that, DSolve can find solution...
Solving differential equations in Mathematica 7.0Hi,all:
Here is the code I want to solve the equation
Eqn1 := f2*(D[z[x], {x, 1}])^2 + f1*(D[z[x], {x, 2}]) + P*(D[y[x],
{x, 2}]) + Psoil;
Eqn2 := z[x] - (D[y[x], {x, 2}]);
sol = NDSolve[{Eqn1 == 0, Eqn2 == 0, y[0] == disp, y'[0] == 0, y[L]
== 0, y'[L] == 0}, {z, y}, {x, 0, L},
MaxSteps -> Infinity, AccuracyGoal -> 10, StartingStepSize -
> 0.001, MaxStepSize -> 0.005,
MaxStepFraction -> 0.001]
f1,f2 are the function of z[x]; Psoil is the function of
y[x];P,L,disp are constant.
and the Mathematica return me the mes...
Bug in Mathematica 6 - Integrate - 27Hello again from the VM machine...
(* K-12 kids know very well that
2 2^z - 2^z = 2^z
2 3^z - 3^z = 3^z
2 4^z - 4^z = 4^z
but Mathematica 6 does not know this. *)
Integrate[1/(2 2^z - 2^z), {z, 0, Infinity}]
Integrate[1/(2 3^z - 3^z), {z, 0, Infinity}]
Integrate[1/(2 4^z - 4^z), {z, 0, Infinity}]
1/Log[2]
1/Log[3]
Integrate[1/(2^(1 + 2*z) - 4^z), {z, 0, Infinity}]
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclop...
solving a system of equations involving numerical integration #2Could someone help me with the following code? I am trying to solve a
system of two equations in two unknowns which involve evaluation of
numerical integrals.
Clear[f];
Clear[g];
Clear[a];
Clear[b];
f[a_?NumericQ, b_?NumericQ] /; a != 0 || b != 0 := NIntegrate[1/(100 +
5*x + 5*y)^0.5*((1/(2*[Pi]* y))*((E^((-((Log[x] - Log[a] - 0.08)^2/2)) -
((Log[y] - Log[b] - 0.02)^2/2)))), {x,0.001, [Infinity]}, {y, 0.001,
[Infinity]}];
g[a_?NumericQ, b_NumericQ] /; a != 0 || b != 0 := NIntegrate[1/(100 + 5*x
+ 5*y)^0.5*((1/(2*[Pi]*x))*((E^((-((Log[x] - Log[a] - 0.03)^2/2)) -
((Log[y] - ...
Solving Third Order differential equation using Mathematica.Hi,
I am trying to solve a third order differential eqn in mathematica.
DSolve[{1/30 f'''[x] - f[x] (2 a^3/(1 - x a)^3 + 1/(1 - x)^3) - 24 a/
(1 - y) (1/(1 - x)^7 - a^5/(1 - ax)^7) == 0, f[0] == 0,
f''[0] == 0}, f[x], x]
I am running this eqn for last 1 hour :/ why does Mathematica take so
much time?
Will Mathematica able to solve this eqn?
Thanks
Amitesh
On 7/20/2012 2:53 AM, amitesh wrote:
> Hi,
>
> I am trying to solve a third order differential eqn in mathematica.
> DSolve[{1/30 f'''[x] - f[x] (2 a^3/(1 - x a)^3 + 1/(1 - x)^3) - 24 a/
> (1 - y) (1/(1 - x)^7 - a^5/(1 - ax)^7) == 0, f[0] == 0,
> f''[0] == 0}, f[x], x]
> I am running this eqn for last 1 hour :/ why does Mathematica take so
> much time?
>
I do not know why. It looks like a hard ODE.
But let start first by fixing few error in your code
1) ax should be a*x
2) a third order initial conditions ODE will have 3 initial conditions
(unless you wanted to obtain constants for these. But since you provided
IC for f[0] and f''[0], then this tells me you missed an IC for f'[0] ?
3) what exactly is 'y' above? this is used as a parameter like 'a'. Then
using 'y' for a parameter is a really bad choice for a symbol. Use 'b'
or 'c'. That is the standard.
4) it is a hard ode. For some conditions on 'a' and 'y', you'll can get ...
Mathematica can't solve simple system of equationsAssume I have two equations a[i]^x(a[i]^x+a[j]^x)^(1/x)-p[i], where
i=1,2, i!=j (not equal), and all variables, {a,x,p} are strictly
positive. Mathematica cannot give me the answer that I can work out by
hand in less than a minute. I used both Solve and Reduce to solve for
a[i], i=1,2. Please advise. Mukhtar Bekkali
On 9/15/05 at 5:16 AM, mbekkali@gmail.com (Mukhtar Bekkali) wrote:
>Assume I have two equations a[i]^x(a[i]^x+a[j]^x)^(1/x)-p[i], where
>i=1,2, i!=j (not equal), and all variables, {a,x,p} are strictly
>positive. Mathematica cannot give me the answer that I ...
Solving on mathematicaHow would i go about solving this equaiton on mathematica
(Xi -Ux)^2 + (Yi - Uy)^2 + (Zi - Uz) = (Ri - Cb)
i = 1,2,3,4
where we need to find Ux, Uy, Uz, Cb tried a few things and they dont work.
NSolve[ (Xi - U)^2 + (Yi - V)^2 + (Zi - W)^2 == (Ri - B)^2, {U, V, W,
B}, { i = 1, 2, 3, 4} ]
any ideas?
Hi Chris,
there is not enough information in your equations to distinguish Uz from
Cb. In your equation they appear always as Uz-Cb. Therefore, either
your equations are wrong or you need to replace the 2 independent
variables Uz and Cb by a single variable...
Solving this in mathematica?I have following code in mathematica:
------------------------------------------------------------
rbar = 0.006236
rt = r_bar
k = 0.95
sigmar = 0.002
betazr = -0.00014
sigmaz = 0.4
pi = 0.99
chi = 0.05
Cbar = -3.7
alpha1[n_] := alpha1[n] = alpha1[n - 1] + alpha2[n - 1]
alpha2[n_] := alpha2[n] = k (alpha2[n - 1])
sigma1sq[n_] :=
sigma1sq[n] = sigma2sq[n - 1] + 2 sigma12[n - 1] + sigmaz^2
sigma12[n_] :=
sigma12[n] = k (sigma12[n - 1]) + k (sigma2sq[n - 1]) + betazr
sigma2sq[n_] := sigma2sq[n] = (k^2) (sigma2sq[n - 1]) + sigmar^2
phi1[n_] := phi1[n] = phi1[n - 1] + phi2[n - 1] + (0.5) (sigmaz^2)
phi2[n_] := phi2[n] = k (phi2[n - 1]) + (1 - k) (rbar)
psi[n_] := psi[n] = phi1[n] - (0.5) (sigma1sq[n])
alpha1[0] = 0
alpha2[0] = 1
sigma1sq[0] = 0
sigma12[0] = 0
sigma2sq[0] = 0
phi1[0] = 0
phi2[0] = 0
B[h_, r_] := Exp[(-alpha1[h]) (r) - psi[h]]
Exp[Cbar - beta] Sum[(Pi^x) B[x, r], {x, 1, 1000}]
----------------------------------------------------------------------
and I am wondering if it is possible to solve the last line such that I have "r" as a function of "beta", satisfying
Exp[Cbar - beta] Sum[(Pi^x) B[x, r], {x, 1, 1000}] = 1
Because ultimately, I would need to integrate a function J[r] over "beta", so if I don't have "r" as a function of "beta", I don't know how to do the integration of J[r].
Thank you!! L.
Leon <leon.he88@gmail.com> writes:
[snip]
...
Re: Why mathematica can't solve this non linear equationHi All,
I need to solve below equation. My PC got stuck.
Solve[{(\[Mu]0 Sin[t - t0])/Sqrt[ l2^2 + \[Mu]0 l2 Cos[t - t0] +
\[Lambda]0] + (\[Mu]1 Sin[t - t1])/ Sqrt[l2^2 + \[Mu]1 l2 Cos[t - t1] +
\[Lambda]1] == 0, (2 l2 + \[Beta]0 + \[Mu]0 Cos[t - t0])/Sqrt[ l2^2 +
\[Mu]0 l2 Cos[t - t0] + \[Lambda]0] + ( 2 l2 + \[Beta]1 + \[Mu]1 Cos[t -
t1])/Sqrt[ l2^2 + \[Mu]1 l2 Cos[t - t1] + \[Lambda]1] + 2/( 1 + V
r^(l2/D0)) == 0}, {t, l2}]
Hi, Norman,
I personally consider this forum to be a place where we exchange our knowledge of Mathematica. My opinion that this is not a place
where one can turn to have
* his job done,
* his homework fulfilled, or
* his scientific problem solved
by somebody else instead of him.
It is understood that people here are rather busy with their own work (at least, a good part of them), and it is only their good will to spend a part of their precious time helping one another.
I give here only my personal attitude. Others will express theirs, if they wish.
Now you posted here several questions, all of the same sort. It looks very much to fit to one of the cases I listed above.
I wish you success in solving your problems yourself, and, of course, feel free asking us questions concerning difficult Mathematica tricks, where we will make our best helping you.
Alexei
Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG
Office phone : +...
Wolfram Research QA process defect: Bug in Mathematica 6(***************************************************************)
If the same bugs exist through numerous software releases,
I think that is valuable public information.
It just should not happen.
-- Brad Cooper
(***************************************************************)
-----------------------------------------------------------------
Daniel Lichtblau tells you how unprofessional I am. Small wonder.
Do not trust him. He is here as a hidden Wolfram Research sales
person talking to you -- to change your mind, to push Mathematica
sales -- as if he is just a non-biased...
[Mathematica 6] Sudden shutdown of Mathematica. No error messages, no traces, no warning. Mathematica just disappears from desktopI've noticed this now more than one time. I would say this has happened to
me about 5-6 times already since I started using Mathematica 6 which is
about 2 weeks now.
This is what happens: I'll be working on an open notebook, and do something,
for example, just now, I went to do SAVE AS to save the notebook.
Mathematica would just disappear in split second.
No errors, nothing. I look and it is just gone. All windows gone. No traces.
I have to restart Mathematica.
And I just lost all my work for the last 30 minutes.
Strange thing is now when I open the document sin...
Wolfram reinvents Mathematica with Mathematica 6Mathematica 6 is now available, introducing over 1,000 groundbreaking
technologies developed over more than a decade at Wolfram Research.
Mathematica 6 takes technical computing to a new level: more tightly
bound, more natural, and more automated, applicable to a far wider
range
of areas than ever before. Central to this achievement is "instant
interactivity"--taking models, computations, or just about any concept
and turning them into fully interactive applications, sometimes within
seconds.
In addition to the new capabilities for instant development,
Mathematica 6 is also optimized for the opposite end of the
spectrum--infrastructure development--and everything in between.
Key new features include:
* Dynamic interactivity, allowing sophisticated interactive interfaces
to be created from single lines of input
* High-impact adaptive visualization for automated creation of
high-fidelity function and data graphics
* Language for data integration, including automatic integration of
hundreds of standard data formats
* Load-on-demand curated data for math, physics, chemistry, finance,
geography, linguistics, and more
* Symbolic interface construction for immediate creation of arbitrary
interfaces from simple programs
* Automated computational aesthetics, with algorithmic optimization
for
visual presentation
Mathematica 6 is available for Windows NT/2000/XP/Vista, Mac OS X,
Linux
x86/Itanium, Solaris UltraSPARC/x86, HP-UX, IBM AIX, and compatible
systems.
For more i...
Debugging Mathematica Code (Mathematica 7)Hello Experts,
I made my fist steps with the Mathematica (so called) debugger and stumbled
immediately. Is there anywhrere a documentation of this tool that is
worth it's name (a criterion which the Mathematica 7 documentatin on debug
surely fails). I've tried a lot, but I'm still at the stage "trial an
error".
Greetings
Mike
"m.g." <mg@michaelgamer.de> wrote in message
news:gl1okn$dpb$1@smc.vnet.net...
> Hello Experts,
>
> I made my fist steps with the Mathematica (so called) debugger and
> stumbled
> immediate...
How can I solve a system of nonlinear equations AND partial differential equations?Hi there,
I have a system of nonlinear equations that need to be solved simultaneously. The result of these equations, then is needed to be incorporated to a system of PDEs. I know that for the first part I can use "Fsolve", and for the second one I can use "pdetool" but I don't know if i want to link them, that is solve all the equations as one system, how that would be possible.
On 10/2/2013 9:34 AM, Roya wrote:
> Hi there,
> I have a system of nonlinear equations that need to be solved
> simultaneously. The result of these equations, then is needed to be
> incorporated to a system of PDEs. I know that for the first part I can
> use "Fsolve", and for the second one I can use "pdetool" but I don't
> know if i want to link them, that is solve all the equations as one
> system, how that would be possible.
I am not sure exactly what you mean. Is it really possible to first
solve the nonlinear equations, then feed the result into PDE functions?
If so, then I think you should do it that way, because solving a larger
simultaneous equation-PDE system is bound to take more time and memory.
And "pdetool" is the graphical user interface for the PDE functions. You
can certainly do everything at the command line if you like, and that
might make it easier to "glue" the two problems together, the nonlinear
equations and the PDE. Take a look at the PDE Problem Setu...