# Tag Info

### Matlab, Mathematica & LAPACK returning 3 different eigenvectors

Seems that you have a duplicate eigenvalue. Thus, you have two eigenpairs $(\lambda_1, x_1)$ and $(\lambda_2, x_2)$ where $\lambda_1 = \lambda_2$. Denote $\lambda = \lambda_1 = \lambda_2$. Let $\alpha$...
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### Numerically solving differential equations, the domain is very long, [0, +10^6), so the calculating time is very long

Actuallly you can scale the variable of the problem into a different interval. Transform $x \in [0,a]$ where ($a=10^6$) to $\xi \in [0,1]$ by the formula $\xi = \frac{x}{a}$. Thus, using the chain ...
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Accepted

• 3,127
1 vote
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### Is there a number base where pi is a rational number?

No, not for any integer base. Irrational doesn't only mean it has infinitely repeating digits (whatever the base may be), it also means that that number cannot be expressed as a ratio of two integers ...
• 126
1 vote

### Question re Maxima, Magma and/or Sage computational language capabilities

I am happy to report that the problem is solved in Mathematica by Christoph Koutschan by using his add-on package "HolonomicFunctions" (https://www3.risc.jku.at/research/combinat/software/...
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1 vote
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### ISING2D with Mathematica. Searching a correct way to compute the heat capacity (mean values over several iterations)

Unfortunately I am not a Mathematica whiz. and in general do not encourage the use of Mathematica for extensive numerical simulations like Ising model or the likes. So I will post some answers ...
• 351
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### Can a second-order ODE be "inconsistent" with its boundary conditions?

It is impossible that finite element or finite difference violate their boundary condition that you imposed. It is not related to the physics of your problem and it's just an issue with your ...
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### Writing a programming code directly from the mathematical formula?

One problem with converting Tex syntax to equations is that it can be ambiguous - the main goal with TeX is typesetting the look, not the actual meaning. If you have many formulas already in TeX, ...
1 vote
Accepted

### Numerical solution of nonlinear thermoconductivity equation

You got good advices in comments, but as it is only 1D problem, you can manage it using fully explicit method with very small time steps. I checked your code in Mathematica and there are several ...
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