Timeline for NDSolve with boundary condition at infinty
Current License: CC BY-SA 4.0
15 events
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| Feb 21, 2019 at 5:12 | history | edited | xzczd♦ | CC BY-SA 4.0 |
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| Jan 30, 2019 at 12:38 | history | edited | xzczd♦ | CC BY-SA 4.0 |
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| Feb 23, 2018 at 12:15 | comment | added | Hugh |
Thanks. The trouble seems to occur in this line aebc = ptoafunc@{ic0, bc}; I sometimes get thousands of equations rather than just a few for the boundary conditions.
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| Feb 23, 2018 at 12:12 | comment | added | xzczd♦ |
@hugh No, the grid index can be approximate number, but do notice the indices should always match, in the sense of pattern matching. (For example, 1/4 and 0.25 won't match. One possible workaround is using abitrary precision number like 0.25`4. )
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| Feb 23, 2018 at 11:50 | comment | added | Hugh | I am trying to solve on a nonuniform grid. Am I correct in thinking that the grid must be made from integers or ratios of integers. I am getting huge numbers of equations from aebc if I don't use integers. | |
| Dec 1, 2017 at 11:43 | comment | added | xzczd♦ |
@hugh You mean a tutorial for pdetoae or FDM? As to pdetoae, I think its usage is straightforward if one has a basic understanding for FDM, but if you still find it confusing, feel free to ask. As to FDM, I recommend reading Chapter 5 of Introduction to Partial Differential Equations by Peter J. Olver. You can also check tutorial/NDSolvePDE in Mathematica document, that tutorial is quite long and somewhat obscure, but at least the first example therein is relatively simple.
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| Dec 1, 2017 at 11:02 | comment | added | Hugh | You have got my meaning about boundary conditions. Thanks. A great tool. Do you have notes or a tutorial describing more detail? | |
| Dec 1, 2017 at 10:56 | comment | added | xzczd♦ |
@hugh 1. pdetoae is not limited to rectangular grid, it can handle all the regular domain (e.g. a circle) in principle. 2. I'm not quite sure about the meaning of "altering the difference equations", but the 2 methods should be equivalent if you mean "eliminating some of the variables from the difference equation system using b.c.", I prefer using the discretized b.c. as additional equations because it doesn't disarrange the variables so the rebuilding process will be easier. 3. Sadly I have no tool for nonlinear problem on irregular grid at the moment.
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| Dec 1, 2017 at 10:15 | comment | added | Hugh | I have just been back through SE and looked at all the references to pdetoae. It is very impressive. What are the limitations? I guess it can only be used on rectangular grids. However, the ability to solve using 'FindRoot' for nonlinear problems is outstanding. In trying to understand the method I think I see that you put the boundary conditions in as additional equations rather than altering the difference equations. Does this come to the same thing? How do you solve nonlinear problems on non-rectangular grids? Can you get something out of the Finite Element Method? | |
| Dec 1, 2017 at 10:08 | vote | accept | Hugh | ||
| Nov 29, 2017 at 13:11 | comment | added | xzczd♦ |
@hugh Actually tutorial/NDSolveBVP has mentioned that, "some initial value problems with growing modes are inherently unstable even though the BVP itself may be quite well posed and stable", and I think your equation system happens to belong to this type. As to the derivative, sadly it's not possible to extract them directly AFAIK. (You see, FDM only solves for the function value. )
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| Nov 29, 2017 at 13:03 | comment | added | Hugh | I have been looking at the output. I am most interested in the derivatives of the solution. I have been interpolating and then taking the derivative. Can the derivative of the solution be extracted from the method directly? The interpolation always adds some numerical noise. | |
| Nov 29, 2017 at 13:01 | comment | added | Hugh | This is wonderful. It is amazing that it does better than 'NDSolve'. I guess that it is the advantage of working on a grid. Many thanks. | |
| Nov 29, 2017 at 12:50 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Nov 29, 2017 at 11:54 | history | answered | xzczd♦ | CC BY-SA 3.0 |