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Topic: highly accurate pde solvers?
Replies: 6   Last Post: Nov 30, 2012 5:34 AM

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Rui Maciel

Posts: 107
Registered: 11/27/05
Re: highly accurate pde solvers?
Posted: Nov 30, 2012 4:51 AM
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Leslaw Bieniasz wrote:

> I need to solve a certain relatively simple PDE
> (evolutionary convection-diffusion in 1D space)
> but with a very high accuracy, ideally with a relative error 10^(-20).


I suspect that such a level of accuracy isn't possible with single and
double-precision floating point types, even if you manage to get the
analytical solution to your PDE. Even the IEEE 754's double extended
floating point data type is only able to express about 19 significant
digits.


> Are there any free programs available that can handle such a problem?
> I presume the programs would have to use some sort of arbitrary precision
> arithmetics.


I don't know of free programs, but I believe Mathematica does support
arbitrary precision numbers.


Rui Maciel



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