# Questions tagged [numerics]

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

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### Numerically computing the eigenvalues of an infinite-dimensional tridiagonal matrix

I have one infinite dimensional tridiagonal matrix whose eigenvalues I have to compute. How can that be done numerically using Mathematica? Let me expose the concrete case I want to do it. I shall ...
1k views

### How to display very small numbers in Mathematica?

I am trying to evaluate the function: $$f(x) = \cos(x) - \mathrm{e}^{-2.7 x}$$ at $x = 1.7 \times 10^{-25}$ and Mathematica keeps returning '0.' How do I evaluate the expression in a better way?
215 views

### Solution or artifact?

I am trying to increase the precision of the code ...
189 views

### Multivariate Newton-Raphson method and FindRoot module [closed]

Let's suppose that we have the following equation ...
180 views

### Does Mathematica gives us a wrong result for the integral of a function including elliptic functions?

Calculus tells us that the differentiation of the integral of a function should be itself, but at least in one case Mathematica answers NO. I feel very confused. The new figure seems to bifurcate at ...
98 views

### Problem with the Inverse CDF of Non-central F Ratio Distribution

In[3]:= n = 5; n1 = 4; n2 = 6; γ = 0.05; α = 1/370; InverseCDF[NoncentralFRatioDistribution[1, n1 - 1, n1/γ^2], 1 - α - (n - n1)/n2] During evaluation of In[3]...
71 views

### Numerical solution to approximate the singular integration using collocation method

I am working to solve "numerically" the following integral equation IE: u[x]=f[x]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,x}]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,1}] ...
130 views

### Recycling solutions of multidimensional NDSolve

Dear wolfram community, I hope my problem is clear and easy to solve. I have already solved the following heat equation over a domain: ...
107 views

### Problems with numerical integration

I tried to plot beam intensity using a function that evaluates a numerical integral, but it didn't work. Here is my code, which did not produce a result. ...
189 views

### Catastrophic loss of accuracy in Orthogonalize

Context In connection to this question I am interested in orthogonalizing known matrices. As a test case, let us consider the definite positive $15 \times 15$ matrix ...
131 views

### Good practice about numerical precision

In one of my calculations, I get -1.11022*10^-16 as one of my eigenvalues for a matrix. It's essentially zero and I suppose I could use SetPrecision to make it zero but I wonder what's a good practice ...
63 views

### Increasing MaxExtraPrecision arbitrarily changes numerical result

I am trying to confirm that a function $f$ satisfies a particular differential equation of the type $D f=0$, for some differential operator $D$. I set $Df$ as Diffeq...
285 views

### Turn the following values into percentage [closed]

I have the following data: {2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017} {5914, 6143, 6182, 18000, 18173, 18344, 18454, 18506, 18800, 19216} My data is already in Matrix form in ...
46 views

### High numerical precision failing [duplicate]

N[(1 - 2*6.674*6*10^13/(6371000*299792458^2))^(0.5), 20] 1. What I expect: ...
180 views

### A numerical boundary conditions paradox

For $(t,z)\in[0,1]\times[-1,0]$ zmin = -1; tmax = 1; and some fields $w(t,z)$ and $y(t,z)$ ...
33 views

### NIntegrate fails with functions that have (necessarily) numeric lists as arguments

I'm not able to NIntegrate a function that has a numeric list as an argument. My original problem involves a compiled function, but a MWE is the following: ...
78 views

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### Wrong divergence with numerical value

this is my first question in this forum. I'm trying to evaluate some complicated function of, say, $x$ near $x=0$ (in order to integrate it later). The problem is that the numerical value of this ...
117 views

### Removing zero dot after solving [closed]

I've a question regarding "zero dots". Im using a lot of calculation in an application which i am building within mathematica. However when i use the output of solve for instant i will not have the ...
162 views

### How to generate repetitive graphs?

I need to create several graph for different values of a parameter $h$. The code is the following ...
39 views

### numerical integration with intermediate variables

I'm trying to perform the following integral, where the bounds of the inner integrals become the integration variable in the next integral. disregarding the stuff in the exponential in the sample ...
I would like to solve the 3 coupled PDEs describing a damped, nonlinear (i.e displacements in the $x$ direction along the beam need to be considered along with the $y$ displacements normally ...