Community RSS Feed https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions in tag Equation Solving sorted by active Define a boundary for heat equation for a 2D surface? https://community.wolfram.com/groups/-/m/t/2392436 Working with NDSolve trying to define a boundary condition that is a function of time. I did this using a piecewise definition in a DirichletCondition statement. But when I run NDSolve it says the statement can not be parsed and is ignored. Is it possible to define a boundary as a function of time using the DirechletCondition statement? I attached a short notebook that provides some code. &amp;[Wolfram Notebook] : https://www.wolframcloud.com/obj/14cd0e73-d41c-4589-954d-9e769624f513 Edward Davis 2021-10-25T15:39:28Z Findroot error: not a list of numbers? https://community.wolfram.com/groups/-/m/t/2392504 Hi, Thank you in advance for taking the time to look at my problem. I would be grateful if you could help me with the code. I&#039;m trying to simulate the transitional values for my model after obtaining steady-state values (k = 871.829). However, this is the error msg I have been receiving all the time no matter what I try (within my limited knowledge): FindRoot[capeq == 0, {k, 871.8287954437363}] FindRoot::nlnum: The function value {-1.013 d[2.]+&lt;&lt;9&gt;&gt;+&lt;&lt;1&gt;&gt;-(1.05 (&lt;&lt;15&gt;&gt;+ &lt;&lt;2&gt;&gt;))/(&lt;&lt;19&gt;&gt;+&lt;&lt;18&gt;&gt;)} is not a list of numbers with dimensions {1} at {k} = {871.829}. The capeq equation as follows, since t = 1 to 30: capeq[t_] = a[1, t] + a[2, t - 1]/(1 + n) + a[3, t - 2]/(1 + n)^2 + a[4, t - 3]/(1 + n)^3 + a[5, t - 4]/(1 + n)^4 + a[6, t - 5]/(1 + n)^5 - d[t + 1]*(1 + n) - (1 + n)* k[t + 1]*(l[1, t] + l[2, t - 1]/(1 + n) + l[3, t - 2]/(1 + n)^2 + l[4, t - 3]/(1 + n)^3 + l[5, t - 4]/(1 + n)^4 + l[6, t - 5]/(1 + n)^5) I hope the above information is adequate for you to help me. Much appreciation for your time. Most humbly, Pema pemma dorji 2021-10-25T10:25:28Z Issue with WorkingPrecision in FindRoot? https://community.wolfram.com/groups/-/m/t/2391287 Hello, I would like to ask about how WorkingPrecision option works in FindRoot. Basically, I have two functions \theta and \phi on a lattice N1xN1. On each site I have two equations like below with some boundary conditions, so I use FindRoot to solve all of them. I&#039;ve got warning message like on second picture and result was not quite physical so I decided to increase WorkingPrecision, but when I change it to whatever except MachinePrecision calculation freezes(I checked 3,6,16,50). As I understood by changing WorkingPrecision I simply change number up to which Mathematica holds the order during computation(maybe there are some nuances like this is order in hexadecimal system but nevertheless), but it looks like there is something else. I would be very grateful if someone can help me. Notebook is attached, I highlighted Findroot with red. ![Equations]![Warning about precision] ![FindRoot itself] : https://community.wolfram.com//c/portal/getImageAttachment?filename=1.jpg&amp;userId=2391255 : https://community.wolfram.com//c/portal/getImageAttachment?filename=2.jpg&amp;userId=2391255 : https://community.wolfram.com//c/portal/getImageAttachment?filename=3.jpg&amp;userId=2391255 Dmitry Kiselov 2021-10-23T14:02:56Z Interpolating functions as output for NDSolve[ ] https://community.wolfram.com/groups/-/m/t/2390685 Working with the pde numeric solvers. If I use a statement like: sol = NDSolveValue[{op == 0, pbc, Subscript[\[CapitalGamma], Dc]}, u, {x, y} \[Element] \[CapitalOmega]] I will get back an interpolating function and I can do things like sol[3,4] to pull values from the function. If I use the form sol = NDSolveValue[{op == 0, pbc, Subscript[\[CapitalGamma], Dc]}, u[x, y], {x, y} \[Element] \[CapitalOmega]] I get back an interpolating function with [x,y] appended at the end. If I try sol[3,3] the output just appends [3,3] to the end. How ever statements like: ContourPlot[sol, {x,-1,4},{y,0,4}] still work. Can someone point me in the right place to understand why the two outputs are different? Thanks Edward Davis 2021-10-22T18:19:14Z Problem using Piecewise with NDSolve https://community.wolfram.com/groups/-/m/t/892695 I&#039;m using an interpolation function defined over a limited range &amp; using &#034;Piecewise&#034; to extend the range. This &#034;Piecewise&#034; function defines the derivative in &#034;NDSolve.&#034; The result seems to be correct, but an error message results indicating that the interpolation function is being asked to extrapolate out of its defined range. I have used &#034;Piecewise&#034; in the past with &#034;NDSolve&#034; without this error. Using &#034;Integration&#034; to integrate the &#034;Piecewise&#034; function doesn&#039;t generate the error message. Here is a simplified version of the code: hf= Interpolation[{{0, 0}, {1, 0.4}, {2, 1.2}, {4.7, 3.4}, {5, 3.4}, {5.4, 3.3}, {9, 1.8}, {12.5, 1}, {16, 0.1}, {17, 0}}, InterpolationOrder -&gt; 1]; h[t_] := Piecewise[{{hf[t], 0 &lt;= t &lt;= 17}}]; ih = NDSolveValue[{ih&#039;[t] == h[t], ih == 0}, ih, {t, 0, 30}] {Integrate[h[t], {t, 0, 30}], ih} Am I doing something wrong? Comments please. Thank you. David Barrows 2016-07-22T21:18:18Z Fixed points of coupled NLD involving transcendental functions https://community.wolfram.com/groups/-/m/t/2389561 I have the Thomas system at hand and want to find out the fixed points of the equation using Mathematica for the whole range of the parameter. The system of equations are $$x&#039;[t]=-b*x[t]+sin[y[t]]$$ $$y&#039;[t]=-b*y[t]+sin[z[t]]$$ $$z&#039;[t]=-b*z[t]+sin[x[t]]$$ where b ranges from 0 to 1. I have tried the following mathematica code, eqns={x&#039;[t]=-b*x+Sin[y],y&#039;[t]=-b*y+Sin[z],z&#039;[t]=-b*z+Sin[x]}; soln=Solve[eqns==0,{x,y,z}] For this I got an error &#034;This system cannot be solved with the methods available to Solve&#034;. How can I solve the above system of equations ? How can I get a full picture of the fixed points? vijay arjun 2021-10-21T05:51:57Z Plotting a function which has eingenvalues of a matrix? https://community.wolfram.com/groups/-/m/t/2389202 I have constructed the elements of the following 4x4 matrix solving some differential equation, namely &#034;sol&#034;: \[Rho][t] := {{Subscript[\[Rho], gg][t] /. sol, 0, 0, Subscript[\[Rho], ge][t] /. sol}, {0, Subscript[\[Rho], ss][t] /. sol, Subscript[\[Rho], sa][t] /. sol, 0}, {0, Subscript[\[Rho], as][t] /. sol, Subscript[\[Rho], aa][t] /. sol, 0}, {Subscript[\[Rho], eg][t] /. sol, 0, 0, Subscript[\[Rho], ee][t] /. sol} } I would like to use the eingenvalues $\lambda_{i}[t]$ of this matrix in the following function: Max[0, Sqrt[\[Lambda] /. einge] - Sqrt[\[Lambda] /. einge] - Sqrt[\[Lambda] /. einge] - Sqrt[\[Lambda] /. einge]] I&#039;ve tried, with no success, the following: einge := Eigenvalues[\[Rho][t]] Plot[Evaluate[{Max[0, Sqrt[ einge] - Sqrt[ einge] - Sqrt[ einge] - Sqrt[einge]]} /. einge], {t, 0, 100}] Can someone help me to found the right way to plot this function? Matheus Soares 2021-10-20T14:12:11Z