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RSS Feed for Wolfram Community showing any discussions in tag Equation Solving sorted by activeWhy does the memory used keep going up and no output is given?
https://community.wolfram.com/groups/-/m/t/3127782
This actually eventually crashed my hard drive, after memory exceeded several Gigabytes. I wonder if it can be improved?
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/7e88b0dc-72e4-4410-b923-eb5cd54f3edfIuval Clejan2024-02-21T22:30:03ZHow to eliminate the divide by zero error in NDSolve by implicit methods on fixed grids?
https://community.wolfram.com/groups/-/m/t/3132715
Hello, it is not my first post about how to use NDSolve for solving PDEs, but unfortunately, I have been unable to make any progress for more than a month. I think I want to accomplish a simple task: solve a certain PDE using exclusively fixed, uniform grids, and observe how the errors diminish when I refine the grids and/or increase discretization orders, and simultaneously increase the working precision. My goal is to obtain the solution having ca. 19 accurate digits. Unfortunately, whatever I do, I get different kinds of errors, and it seems nobody can tell me how to proceed. Is there noone there, in this list, who knows how NDSolve works? Maybe some authors of the marvel called NDSolve?
I now try to solve a PDE of the nonlinear reaction-diffusion-convection type, in which there is a coefficient standing at the temporal derivative (y is the temporal variable), which becomes zero when y=0. For this reason, I decided to use ImplicitRungeKutta methods. As far as I understand implicit methods, they should sample the PDEs at y>1, but never at y=0, so that there should be no problem with obtaining the solutions. But I get error messages stating that there are divide by zero errors. Here is my code:
ClearAll;
y0=0;
wmax=10;
ystep=1/10;
difford=2;
wprec=8;
pdesol=NDSolve[{D[psi[w,y],{w,2}]+2*w*D[psi[w,y],{w,1}]-4*y*(1-y)*D[psi[w,y],{y,1}]-4*(psi[w,y]^2-psi[w,y])==0,psi[w,y0]==Erf[w],psi[0,y]==0,psi[wmax,y]==Erf[wmax]},psi,{w,0,wmax},{y,y0,1},WorkingPrecision->wprec ,Method->{"FixedStep", Method->{"ImplicitRungeKutta","DifferenceOrder"->difford}},
StartingStepSize->ystep,
Method->{"MethodOfLines","DifferentiateBoundaryConditions"->true,"SpatialDiscretization"->{"TensorProductGrid", "MaxPoints"->20, "MinPoints"->20,"DifferenceOrder"->2}}];
What should I do to get at last the results I need? How to eliminate the divide by zero errors?
I know, of course, that I can select y0 not identical to zero, but equal to some small value, but this causes other error messages, depending also on the choice of other parameters. Some of these error messages suggest that my choice of MinPoints and MaxPoints is ignored, and NDSolve uses
10000 grid points for unclear reason. So, I am also not sure whether I really have fixed uniform grids.
If ImplicitRungeKutta methods are not suitable, than what other kind of fixed grid implicit methods can be used for my purpose? I mean here built-in methods, as I expect devising my own procedures would be much more difficult.
LeslawLeslaw Bieniasz2024-02-29T11:32:55ZError generating graph based on Reduce function result
https://community.wolfram.com/groups/-/m/t/3132522
Hi.
I tried to see whether this equation is positive, and I couldn't find out the best way.
equation: (-2 a (-2+b)^2 (1+b) c+c^2 (2 b^3+8 \[Alpha]-6 b^2 \[Alpha]))/(2 (-4+b^2)^2)
* Question:
What is the correct way to generate a graph with several conditions?
* Condition:
a>c, c>0, 0<b<1, alpha>1
* Attempted Code:
RegionPlot[(c (-a (-2+b)^2 (1+b)+c (b^3+4 \[Alpha]-3 b^2 \[Alpha])))/(-4+b^2)^2 <0,{\[Alpha],1,10},{b,0,1},{c,0,3},{a,4,9},PlotLegends->"Expressions"]
Reduce[-((c (-1+\[Alpha]^2) (a (-2+b)^2 (1+b) \[Alpha]+(-4+3 b^2) c (1+\[Alpha]^2)))/((-4+b^2)^2 \[Alpha]^3))<0&&a>0&&0<b<1&&c<a&&\[Alpha]>1,{\[Alpha]},R]]
Plot[f[\[Alpha]],{\[Alpha],1,10},PlotRange->All]
(FunctionInterpolation[#1,{a,4.,10.},{b,-2.,2.},{c,0.1,3},{\[Alpha],1,10}]&)[-((c (-1+\[Alpha]^2) (a (-2+b)^2 (1+b) \[Alpha]+(-4+3 b^2) c (1+\[Alpha]^2)))/((-4+b^2)^2 \[Alpha]^3))]
I even tried to fix parameters and just want to see how move when alpha is increasing.
but it did not show any result.
Please help me.
Attempted Code:
a = 10;
c = 3;
b = 0.9;
f(\[Alpha]) = (-2 a (-2 + b)^2 (1 + b) c + c^2 (2 b^3 + 8 \[Alpha] - 6 b^2 \[Alpha]))/(2 (-4 + b^2)^2);
Plot[f[\[Alpha]], {\[Alpha], 1, 9},
PlotRange -> All,
Frame -> True,
AxesLabel -> {"\[Alpha]", "f(\[Alpha])"},
LabelStyle -> {FontFamily -> "Arial", FontSize -> 12}]Tchun Jeeyoung2024-02-29T03:39:04ZColloquium event - numerical methods for partial differential equations and their applications
https://community.wolfram.com/groups/-/m/t/3132386
![enter image description here][1]
In this special online colloquium, we have invited researchers from around the world to share their recent exciting work. The topic of the inaugural event in this series is "Numerical Methods for Partial Differential Equations and Their Applications". The works shown range from new quantitative methods, to new real-world applications, to novel ways of modeling. The event also begins with a very brief introduction to [PDE Models][2] in the Wolfram Language that introduces functionality new to Version 14.
The (estimated) start time for each presenter can be found in the cloud notebook here: [Link][3].
To register for the event please follow the link to the BigMarker platform found below.
> [**Register Here**][4]
Please feel free to use this thread to collaborate and share ideas. Also let us know what colloquium topics interest you for future events in this series!
![enter image description here][5]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fem-promo.png&userId=2643831
[2]: https://reference.wolfram.com/language/PDEModels/tutorial/PDEModelsOverview.html
[3]: https://www.wolframcloud.com/obj/jmcnally0/Published/Feb29Colloqium-Schedule.nb
[4]: https://www.bigmarker.com/wolfram-u/numerical-methods-for-pde-and-applications?utm_bmcr_source=community
[5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUbanner.png&userId=2643831John McNally2024-02-28T21:41:17ZSolving a system of three fractional order differential equations in the sense of Caputo
https://community.wolfram.com/groups/-/m/t/3131676
Hello everyone,
I hope you are in good health.
Here is a system of three fractional order differential equations, I am trying to solve it in the sense of Caputo.
The syntax is correct as it is advised in the documentation but still I cannot get the solution, I do not know what is incorrect.
I need help, it will be highly appreciated.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/a587a53d-965b-4c0c-addc-e7c7eee5c0c0Burhanuddin Safi2024-02-28T11:02:05ZKinematic analysis and animation of a quick return mechanism with differential equations
https://community.wolfram.com/groups/-/m/t/3131236
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=QuickReturnMechanism.gif&userId=20103
[2]: https://www.wolframcloud.com/obj/7f777711-0b41-422c-b068-869802e45aaaDavid Balandra2024-02-27T08:37:34ZIterating SolveValues for a function using For?
https://community.wolfram.com/groups/-/m/t/3129320
Hi, everyone! Honestly, I have learned right now how to use this dialog box. Thank you, Eric Rimbey!
Well, my problem is about using the FOR loop in the following case:
f[x_,y_]:= x - 5*y - 10;
v1={};
For[y=1,y<=10,y++,s=SolveValues[f[x,y]==0,x,Reals];AppendTo[v1,s0]]
There is something wrong with this code, because s has not been evaluated at each iteration.
If there is a better way to solve with Wolfram functions, I would love to know about that.
Please, help me out in dealing with this issue. Thank you in advance for your help.Edson Orati2024-02-23T18:31:42Z