Here 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 ...

Mr 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...

To 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...

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) =...

Hi, 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 ...

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,...

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...

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...

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}] 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. ...

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...

Hello, 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...

Hi,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...

Hello 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...

Could 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] - ...

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 ...

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 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 ...

How 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...

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] ...

Hi 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 : +...

(***************************************************************) 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...

I'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...

Mathematica 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...

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...

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...

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