DSolve does not solve this

Questions
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1

Hi all,

I am switching from Maple slowly to Mathematica. Here is a PDE problem, which is sovable in Maple, but I can’t seem to get it work in Mathematica. This is just a “small” example I took.

In my work sheet, I have attached the problematic PDE.

I am not sure whether it’s the double subscripts that I have used, so I tried to change to a set of simpler variables.

For those who are instersted, I have also attached the “solution” from using Maple (PDF format).

FF = f[a, b, c, d]
eq1 = D[FF, d] + (1 - a)*D[FF, a]/d == 0
eq2 = D[FF, c] + (b - (a - 1)*d)*D[FF, a]/(c*d) == 0
eq3 = D[FF, b] + D[FF, a]/d == 0
DSolve[{eq1, eq2, eq3}, {FF}, {a, b, c, d}]

And I expect Mathematica to give something like a valid solution, such as (from Maple)

FF = (-b + (a - 1) d) c

Many thanks!

2

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3

Hi Udo,

I dont know much how PDE (or DE). But say if I just want to get something like the output from Maple (see the Maple PDF), is that possible?

So f is a function:

f = (-b+(a-1)d)c

and it is a valid solution to this system.

Many thanks!

4

Frankly spoken, I do not see it. The net knows, that one has to tinker a bit in the case of a partial differential equations system under Mma, compare e.g.

http://mathematica.stackexchange.com/questions/42326/how-to-solve-a-system-of-partial-differential-equations

there is also an informative manual from Wolfram Research

http://www.google.ch/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDcQFjAB&url=http%3A%2F%2Fwww.wolfram.com%2Flearningcenter%2Ftutorialcollection%2FDifferentialEquationSolvingWithDSolve%2FDifferentialEquationSolvingWithDSolve.pdf&ei=aOJlU-jSN6mh0QWZy4C4BA&usg=AFQjCNEjW4Lug2dR5_fShPwL7gBFVStCNA&bvm=bv.65788261,d.bGQ

if not successful on the direct way, one does usually the following: make an educated guess (* a so called ansatz *) and solve the ansatz. Actually one would do a power series in four variables, producing recurrence relations for the coefficient a[n1,n2,n3,n4] and trying to solve them using RSolve[].

5

Hi Udo,

Yes, I knew that manual you were referring to. However, it is only a “small” system i used to adress the problem here. I have many and much larger PDE systems, which were formed from my research problems. So I dont think my focus is on the PDE here. If I have the time, I will stick with Maple for this matter. Because Maple works.

I tried the example on stackexchange. In my case, it does not work. Again, it’s just not what i was expecting. I want something simple so I can apply it to many other (similar) PDEs.

Many thanks for your help though!!

6

Mathematica does not currently solve these type of problems, which we’re very much aware of.

In Mathematica 10 we have introduced a wide range of new capabilities to DSolve and related functionality, these can be exposed by the “Show changes” button here: DSolve: Solve a differential equation—Wolfram Documentation

Providing analytical and numerical solutions to differential equations continues to be an important component of our research and development, this family of problems is of particular interest to us and will be the focus of future updates to the Wolfram Language and Mathematica functionality.

7

Hi Martin,

Thanks for your comment.

Yes, I have tried this particular system in MMA 10, but it still does not perform as expected.

I am in general very much like to explore more in MMA. But for my research purpose at the moment, I will have to stick with Maple, because it is the only Computer Algebraic package that gives me what I need. The PDEs actually form from a null space of particular matrices. So in practice, I demand much more than this “simple” and small example.

It would be nice to see more of this development in the future.

Chen

8

Any update on this PDE?

Thanks!