Questions tagged [numerics]

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

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5 answers
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How to solve the minimum value of a function without analytic expression?

The analytic expression can be obtained for f. f = Integrate[AiryAi[x], x] -((x (-3 Gamma[1/3] Gamma[5/3] HypergeometricPFQ[{1/...
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0 votes
0 answers
22 views

How to plot a function that depends on a solution to a numerical equation?

Consider a function H[q(t),r(t)] = (1/2)(f[r(t)]-f[q(t)]), where f(x) is known, r(t) depends on q(t), and q(t) is a solution of a numerical equation. Question: How do I plot H(t)?
0 votes
1 answer
52 views

Representing a number in r0 + r1 E + r2 E^2 form

Let E be the base of natural logarithm 2.71... A Sequence S[n] is believed to converge to a ...
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0 votes
1 answer
120 views

NIntegrate: slow convergence error and speed efficiency [closed]

I am trying to produce a plot but NIntegrate is very slow and making a number of warnings, I have used UnitStep[] to keep the ...
6 votes
2 answers
661 views

NDSolve very slow on 2D heat equation

I am trying to solve the 2D heat equation $$ \begin{cases} u_{t}-u_{x x}-u_{y y}=f \\ u(0, x, y)=\sin (2 \pi x) \sin (2 \pi y) \\ u(t, 0, y)=0 \\ u(t, x, 1)=0 \\ u_{x}(t, 1, y)=2 \pi e^{-t} \sin (2 \...
0 votes
0 answers
46 views

How to increase the precision of numerical derivatives?

I need to make sure about precision of numerical derivatives in my calculations. I use finite element method to obtain a wave function, then I take derivatives of this numerical wave function to get ...
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0 votes
0 answers
61 views

Implement of Euler Method of Parabolic PDE

I'm experimenting with different schemes for numerically solving PDEs in Mathematica. I use NestList to implement the Euler Method for 1-D PDE, the code is concise: ...
0 votes
0 answers
40 views

Finite Difference and LinearSolve

I have two nonlinear second order coupled boundary value ODE whose dependent variables are $u(x)$ and $z(x)$. I want to solve it using the Relaxation method (Finite-Difference), however, I can't ...
0 votes
0 answers
35 views

Numerical integration converging too slowly with Tanhyberbolic function

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0 votes
1 answer
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Why does an error occur in one case, but not in the other, and how to fix it?

Why do errors appear for this Kx[11, 15] when this Kx[11, 14] is considered without error? How to fix it? ...
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6 votes
2 answers
76 views

How to pass solution of ParametricNDSolve to NSolve

I am taking here example ParametricNDSolveValue problem from documentation ...
1 vote
1 answer
45 views

Finding numerically roots of equation over region

I'm trying to solve the following numerical problem: I have a function of 2 variables in some rectangular region, the function is computed numerically with some moderate time cost (solution of linear ...
0 votes
1 answer
51 views

Make a list for n from 2 to 10 of array plots for x and y up to 50 x^y mod n [closed]

Table[ArrayPlot[Mod[x, y, n]], {n, 10}, {x, 1, 50}, {y, 1, 50}] expected answer [
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2 votes
1 answer
57 views

Finding the root of a scalar function of 3 variables which is a an interpolation of data?

Dear Stackexchange community, I am puzzling the following question: I have energy values on a three dimensional grid. More precisely, I have the solutions from a band structure calculation on a three ...
1 vote
2 answers
160 views

Accurate NDSolve for PDE with NIntegrate Functions

I have a function $A(c)$ which is defined by an integral. I wasn't able to solve it analytically, and therefore defined $A(c)$ using NIntegrate: ...
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5 votes
3 answers
234 views

How can I transform the list into the required form?

I have the list: List1={{7, {-0.91, {a -> 0.61}}}, {10, {-1.41, {a -> 0.44}}}, {12, {-2.00, {a -> 0.35}}}, {15, {-2.69, {a -> 0.28}}}} I ...
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0 votes
1 answer
63 views

Why, if you write the expression in the form of two functions, does the code stop working?

I would like to find the minimum of the function EER[a, v] using parallel computing. If I write the code like this, it works: ...
  • 615
3 votes
1 answer
195 views

Coiling of flexible ropes (nonlinear BVP of ODEs with 10 unknown functions and 2 parameters)

I want to solve this ODEs with NDSolve, but it fails. The $F$(F), $\gamma$ (γ) is the given ...
1 vote
1 answer
144 views

Why is there an error in one case and not in the other?

Why does the error occur for P[34, 14] whereas for P[33, 14] has no error? How to get rid of this error? ...
  • 615
1 vote
0 answers
64 views

Why does the minimum eigenvalue sharply decrease when the number of basis functions increases from 37 to 38 and more?

I have the following Hamiltonian: H = -1/2 * Laplacian -1/r - 2 * r/5 * (Exp[-r * 1.6] + Exp[-r * 3.1]) I'm trying to find the minimum eigenvalue of this Hamiltonian using the matrix method. As basis ...
  • 615
2 votes
2 answers
158 views

NIntegrate gives the wrong result

I have tried to calculate an integral of a function numerically using NIntegrate, but sadly it seems like I do not get the correct result from it. The function $\...
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14 votes
1 answer
257 views

What Reap/Sow tricks do you use?

I admit that I have been reluctant to use Reap and Sow for years and that I used it only when I had no choice with ...
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1 vote
1 answer
128 views

Eigenvalues of Coulomb potential

As it turned out in the previous question (Eigenvalues of A/r^2 + B*r^2 potential), in order to find the energies by the matrix method, it is necessary to have a complete set of basis functions. @...
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3 votes
1 answer
37 views

How to troubleshoot NIntegrate non-numerical error?

I am trying to evaluate a 2d integral (denoted as x and y here) with a function that involves a numerical integral at each point....
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0 votes
1 answer
46 views

Is the equality correct? [closed]

Is the equality above correct where q satisfies |q|<1 ? If it is, how to prove it?
2 votes
1 answer
104 views

Eigenvalues of A/r^2 + B*r^2 potential

I would like to find the energies of a system in a matrix way. The system has the following Hamiltonian: H1 = -1/2Laplacian +(A1/r^2)+(B1r^2) I use radial functions as basis functions: Psi1[r_, n_] =...
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1 vote
1 answer
216 views

Why Wolfram 12.1 not calculated? [closed]

Why doesn't scientific software count, ...
0 votes
1 answer
113 views

Why do different calculations give different eigenvalues?

I find the eigenvalues of the Hamiltonian in two ways - numerically and matrix . Why do different calculations give different eigenvalues? The Hamiltonian is H = -1/2*Laplacian -(2/r) It can be seen ...
  • 615
1 vote
1 answer
59 views

Equality contraint violated with NMinimize

I am attempting to numerically optimize a function of only 2 parameters k, θ. There are two inequality constraints (1 each on k ...
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3 votes
6 answers
612 views

How to ask Mathematica to compute the given sum of the differences of the numbers of the given two sets?

I have two sets of real numbers, say, set1= {b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11} ...
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3 votes
2 answers
112 views

1D ODE: singularity or stiff system suspected

I'm trying to solve the nonlinear Poisson-Boltzmann equation in a cylindrical geometry. In this example I am surrounding a central charged rod with a neutralizing shell of charge, although I get the ...
1 vote
2 answers
103 views

NMinimize keeps returning Indeterminate for well defined function

I am attempting to numerically optimize a function of only 2 parameters k, \[Theta]. The function is well-defined and the constraints are simple. However, the ...
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4 votes
1 answer
125 views

How to know the minimal mesh size of NIntegrate?

Sometimes it is necessary to know the discretization mesh size in numerical integration. But since NIntegrate is a complicated composition of various algorithms, it ...
  • 4,532
1 vote
2 answers
122 views

Trying to apply numerical method with Do

I am trying the following scheme to learn to implement an iteration using Do loop. I tried to implement the same method using for loop but with same errors. I, therefore, turned to the Do loop to ...
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2 votes
1 answer
143 views

How to avoid infinities in the following example?

The task Consider a decaying particle traveling along some axis $x$, with the differential probability to decay given by the Poisson distribution: $$ \frac{dP_{\text{decay}}}{dx} = \frac{\exp[-x/l_{\...
  • 4,458
3 votes
2 answers
163 views

Non-linear integro-differential equation with infinite domain of integration

$$I(t)=\frac{dy(t)}{dt}+\int_{-\infty}^t dt'\left[\sin\left(\frac{y(t)-y(t')}{2}\right)f(t-t')-\sin\left(\frac{y(t)+y(t')}{2}\right)g(t-t')\right]$$ with $y(t\leq 0)=0$ and $I(t)=I_0\Theta(t)$ with $\...
0 votes
0 answers
61 views

How to get a result for some values of parameter H

This is my code. ...
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1 vote
0 answers
106 views

How to simplify/express the given number in a compact rational form?

I have the given number; using N[numb], I can find its approximate value but I want to simplify it in a short compact rational form (containing a trigonometric ...
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1 vote
0 answers
49 views

Mathematica incorrectly claims an infinite sum doesn't converge

When I compare the output of the following commands I get contradictory results: Sum[BesselJ[k, 1], {k, 0, Infinity}] NSum[BesselJ[k, 1], {k, 0, Infinity}] The ...
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10 votes
2 answers
267 views

How to monitor the progress of LinearSolve?

I am trying to do something like ...
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2 votes
2 answers
76 views

How to speedup comparison in the following example?

I have the following problem: I would like to generate random values of some variable $z$ obeying some distribution, but simultaneously within the interval zmin<...
  • 4,458
1 vote
1 answer
67 views

Speed up summation of many inverse matrices

Physical background I am trying to write a code that computes the Green function of a system, given the Self energy $\hat{\Sigma}_n$, a list of Matsubara frequencies $z_n$ ($n=1,...,N_{Mats}$) and the ...
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1 vote
1 answer
57 views

Strange behaviour of IntersectingQ

I wanted to check whether two lists of complex numbers have an element in common and stumbled upon this rather strange behaviour of the function IntersectingQ. If I ...
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0 votes
0 answers
51 views

How to solve a delay partial differential equations numerically?

A set of special partial diffential euqations like this: $$\dot{O}_x=\textrm{i}\cos^2(\tau)\partial_\tau O_y+\alpha O_x(\tau=0,t)O_z-\frac{O_x}{T_2}$$ $$\dot{O}_y=-\textrm{i}\cos^2(\tau)\partial_\tau ...
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1 vote
1 answer
80 views

Inconsistent results solving system of equations with FindRoot

I have been trying to solve the following problem (Is basically a physics problem: an expansion of equations of state up to 1st order of the order parameter in order to solve for the critical ...
1 vote
2 answers
240 views

How to prevent Mathematica from rounding some PDF values to 0?

Dear Mathematica community, I'm having a problem with the PDF function for the hypoexponential distribution. Specifically, Mathematica returns 0 as soon as the value is very small. Below is an example:...
2 votes
0 answers
76 views

Z-eigenvalue problem

I am interested in solving an $N-$dimensional $Z-$eigenvalue problem, which schematically takes the following form $$ \sum_{b=1,c=1}^{N}T_{abc} X_b X_c=\lambda\,X_a\quad \text{with}\quad \sum_{a=1}^...
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1 vote
2 answers
89 views

Smooth out numerical fluctuation at known point

I have the following function ...
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0 votes
1 answer
65 views

How to avoid General::munfl errors?

Let's have a look at a following system of equations: ...
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1 vote
0 answers
76 views

Kahan Compensated Summation

Is there an example/library that implements Kahan summation in Mathematica for matrix-matrix/vector-matrix multiplication? Having some trouble adapting something like this Compilation of Total with ...

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