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Mar 6 |
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2D Heat equation: inconsistent boundary and initial conditions @DanielLichtblau. yes. Please see this page 12000.org/my_courses/UC_davis/fall_2010/math_228a/HWs/HW3 I used M for this course (it was a graduate course in numerical PDE's at UC Davis). On the above page you'll see the PDF file of this document a little down the page. |
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Mar 6 |
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2D Heat equation: inconsistent boundary and initial conditions btw, doing Neumann B.C. can be tricky in finite difference. I spend sometime to write a note on this since I kept making mistakes in it. Here is the note, it shows how to discretize 2D for Neumann on the different edges. This is only useful for someone doing FDM by hand ofcourse, not using NDSolve : 12000.org/my_courses/UC_davis/fall_2010/math_228a/HWs/HW3/… |
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Mar 6 |
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How can I control Dynamic property? @halirutan I assumed when I saw the code that the tab setting in Subbu notebook was misconfigured somehow of he might have changed the setting there to his preference as I never seen M generate such large spaces before. I agree, it makes the code harder to read and understand. |
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Mar 6 |
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How can I control Dynamic property? hi; is is possible to make a smaller example that illustrate the problem? Actually, many times I find myself, when I want to ask a question, I go to make a small example to show the problem, and when making this small example, I end up finding my problem, because I eliminated many things that made it hard to see the problem, or by just making the small example to reproduce it, it helped me learn what the problem was. May be you can try that? |
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Mar 6 |
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2D Heat equation: inconsistent boundary and initial conditions +1 good find! But this makes one wonder if M error message in this case could have been made more helpful to users. Since M knows the B.C. is Neumann, and so internally it must have gone through this code path. Then why not make a more informative error message in this case? This would have saved the user much time. WHat I mean, it says This happens due to discretization error in approximating Neumann boundary conditions So, M knows the error! then why not issue this error instead of one given? |
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Mar 6 |
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Plotting Energies vs. m for all values of R with the colors of the levels indexed by R So it looks like you 2 degrees of freedom then. R and m are the independent variables, and the dependent variable is the energy. So your energy(R,m) is a function. So you need 3D plot. The x-axis will be R and the y-axis will be m, and the z-axis is energy(R,m). There are many ways to make 3D plots in M depending on how you want to visualize the result. |
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Mar 6 |
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PlotLegends in ListContourPlot for triplet of data showing strange numbers Since you are on Linux and we both have same version of M (9.0.1) then it must be a bug in the linux version, as I do not see it on windows. But lets wait for others to see. |
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Mar 6 |
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Copy and pasted graphics are fuzzy @Szabolcs I found that if I simply take screen shot, then use PAINT.EXE to grap the screen shot image, then save that to .png, then use the .png in my Latex document, I get the best picture. Strange that if I select the cell in M, then do FILE->SAVE SELECTION AS->PNG, I get bad quality .png comparse to just doing screen shot. I am on windows 7, using M V 9.01 This happens all the time, regardless of the plot I am trying to export from M to Latex. |
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Mar 6 |
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PlotLegends in ListContourPlot for triplet of data showing strange numbers fyi, these side numbers do NOT show up in V 9.01. Screen shot: !Mathematica graphics I am on windows 7 |
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Mar 6 |
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Collecting roots of different equations and create a list Yes, you need to use Flatten if you have lists of solutions in there. I did not show Flatten for FindRoots examples, but did for Solve examples. |
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Mar 6 |
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Collecting roots of different equations and create a list I just picked one point to find root near, which is one. This was to make up some example. I do not know what is your code doing. May be you can post your code in your question, making sure it runs clean. Then one can use your code to show the steps. i.e. just post the equations and the FindRoot command used. What you posted before does not run. Need to post complete self contained code. |
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Mar 6 |
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Collecting roots of different equations and create a list You can use Select or Cases to filter out real roots. Please see update |
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Mar 6 |
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Collecting roots of different equations and create a list added 100 characters in body |
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Mar 6 |
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Collecting roots of different equations and create a list added 287 characters in body |
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Mar 6 |
revised |
Collecting roots of different equations and create a list added 287 characters in body |
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Mar 6 |
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Collecting roots of different equations and create a list Yes, sure. please see update |
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Mar 6 |
answered | Collecting roots of different equations and create a list |
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Mar 6 |
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Copy and pasted graphics are fuzzy may be you can make the example code more complete by adding the line that generated the residualsdata |
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Mar 6 |
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2D Heat equation: inconsistent boundary and initial conditions the IC and BC look to be consistent. But something to look at, your I.C. lead to $k\left( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}\right) =-5k\pi^{2}\cos\left( \pi x\right) \sin\left( 2\pi y\right) $. Hence from the pde itself, this means at $t=0,\frac{\partial u}{\partial t}=-5k\pi^{2}\cos\left( \pi x\right) \sin\left( 2\pi y\right)$ Now see if this is consistent with the B.C.'s shown. I could not find conflict. But it could be becuase you have neumann boundary conditions at the 2 other sides, it could not verify the consistency there, that is all. |
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Mar 5 |
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How is the Mathematica kernel structured internally, and how does evaluation work? You are mixing things. Java is open source. The source code is there to see and for any one to read. The internals of the JVM itself is all there to see. There is a whole book on Java VM. Mathematica is closed source. So all what you can learn about its internals, is whatever we are allowed to see through the glass windows, that is all. Also see Why You Do Not Usually Need to Know about Internals reference.wolfram.com/mathematica/tutorial/… |
