# Tagged Questions

Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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### Finding all/most roots of a discontinuous function more consistently?

I have the equation: f[x_]:=α Tan[α*a] - Sqrt[c - α^2] and ideally I want to find all of its positive zeros, given a and c, with variable alpha. The problem is ...
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### intersection between two curves in Mathematica

I have two curves (drawn from points) in a plane, one is drawn with ListLinePlot and the other drawn with ParametricPlot. How ...
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### How can I handle curve singularity in this NIntegrate integration?

Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region. (Why ...
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### Why does this numeric integral fail to converge?

I have an integral over a region (rpp): ...
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### How to calculate an integral of an expression that is determined numerically (in Mathematica)?

First of all, I am fairly new to Mathematica and Stackoverflow, so please feel free to give me any advice whatsoever. I aim to calculate an integral of an expression that has been determined ...
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### Forcing FindRoot to return only real solutions

FindRoot documentation reports that if the equation and the initial point are reals, the solutions are searched in the real domain. However, in the following case I ...
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### Rounding values [duplicate]

In Mathematica 8 when I enter 1 - 0.99 - 0.01 I get 8.67362*10^-18 instead of zero. How do I fix this problem? I am getting ...
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### Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
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### Numerically solving PDE with high precision

I want to numerically solve the PDE $\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$ with some initial and boundary conditions and given parameters $c$, $m$ and $l$. Consider the code ...
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### Is Abs[z]^2 a bad way to calculate the square modulus of z?

For a numerical quantity z, Abs[z] returns the square root of the sum of the squares of the real and imaginary parts of ...
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### Implementation of Incomplete Fermi-Dirac Integral in Mathematica

I'm working on a special algorithm to implement a more accurate effective mass calculation for hole carriers in silicon in Mathematica. This rather involved algorithm uses incomplete Fermi-Dirac ...
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### RandomReal closed on left & open on right?

I have a number of algorithms that depend on uniform random reals in half-open intervals such as $[0,1)$. In particular, I need a (pseudo) random-number generator that produces machine-precision ...
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### Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
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### Mathematica NDSolve and 'Compile'?

Since the consensus is usually that NDSolve speeds fares badly against compiled code such as c++ ODE solvers using GSL say, is it possible to make up for this lag ...
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### Preventing Numerical value from being evaluated

I have searched stackoverflow (and comparable pages) for quite a while now (got redirected from there to this specialized stack), and I surrender. I am trying to evaluate an expression that is small ...
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### Why is NDSolve solving in term of two 1st order ODE slower than 2nd order?

As mentioned in the documentation for NDSolve it's often convenient to reduce a 2nd order ODE to a system of first order equations. When I do this however I seem to see a significant speed reduction ...
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### NDSolve runs out of memory

I need to solve a second order ODE numerically. The ODE depends on two parameters (a,b). Things work fine when 'a' is small, but for large 'a' the solutions are oscillating rapidly and Mathematica ...
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### How to build a grid of integrand points and numerically integrate?

If I have some function I know numerically only, say f(x) and each point $x$ takes significant time to compute so I have them all stored in some file as f(1)=0.232423, f(1.1)=0.3243432,....Then is it ...
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### NDSolve with Euler method

I want to solve this equation with NDSolve[] using the Euler method: x'[t] == 0.5*x[t]-0.04*(x[t])^2 with initial condition ...