Questions tagged [numerics]

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

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How to include impulses in differential equations?

I have two coupled differential equations as follows: $$S'(t) = - \frac{a}{1 + B(t)} S(t),$$ $$B'(t) = \frac{c}{1 + S(t)} B(t) (1 - B(t)) - d B^2(t) \Big( \frac{1 - B(t)}{B(t)} \Big)^n,$$ where $a$, $...
Tim's user avatar
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Plotting an integral with solving for a specific constant [closed]

Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
Med Ch's user avatar
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Method to make this complicated integration from interpolating function? [closed]

Hello I want to do this integral Mu[Psi_, R_] = Integrate[ D[Integrate[Rp f[Psip, Rp]/Sqrt[R^2 - Rp^2], {Rp, 0, R}], R]/ Sqrt[Psi - Psip], {Psip, Psi0, Psi}] ...
Rémy Galli's user avatar
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71 views

Triple Summation Calculation Which Includes an Integral

I am a beginner in Mathematica. I have to calculate the following summation:$$C_3(\alpha)=\frac{1}{3}\sum_{j,k,l=3}^{\infty}(2j+1)(2k+1)(2l+1)(C_jC_k+C_kC_l+C_lC_j)f_{jkl}$$ where $$f_{jkl}=\frac{1}{4\...
Rosstopher's user avatar
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1 answer
160 views

Using ParametricNDSolveValue and MultiNonlinearModelFit to fit an ODE system to datasets

I asked a question here about fitting an ODE system to given datasets. The great answer of @ydd solved the problem nicely. In the mentioned answer, the initial values are taken as the initial points ...
Tim's user avatar
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When does arithmetic with approximate numbers not follow basic properties?

Consider this: x = Exp[3.5*^15] (* OVerflow[] *) The above is well documented and so is the next result. ...
Ted Ersek's user avatar
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Modeling experimental data with differential equations

I have the following two sets of experimental data, which show the dependencies of two quantities, namely, $S$ and $B$, on time ($0$ h, $3$ h, $6$ h, $9$ h, $15$ h, $18$ h, $21$ h, and $24$ h): ...
Tim's user avatar
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How to solve the following integrodifferential equation by generic approach?

Consider the following equation: $$ \frac{\partial f}{\partial t} - p H(t)\frac{\partial f}{\partial p} = \mathcal{I}[p,t], \tag 1 $$ Here, f = f[p,t], with p being ...
John Taylor's user avatar
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Possible bug in Eigensystem

I'm getting some very strange behavior when running Eigensystem on a 8000 by 8000 matrix of Real numbers (stored as a dense matrix ...
kacper's user avatar
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Why dont I get the numeric value? [closed]

For the given expression: ...
Lelouch's user avatar
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1 answer
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How to solve this integral equation numerically?

I am encountering difficulties while trying to numerically solve an equation in Mathematica that involves an unknown function and an integral. Specifically, the equation takes the form of \begin{...
dcmpsr's user avatar
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2 answers
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Solving A System of Two Implicit Equations

I am solving a system of 6 equations, and I am interested to know the solution for different rhoBar values. Here is the input parameters: ...
joe's user avatar
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3 answers
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Multiple solutions from NSolve

I have a list of polynomial equations which I can solve using NSolve. However, it gives me a large number of similar solutions. The solutions are largely identical ...
Hugh's user avatar
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Plot after applying NIntegrate

I'm trying to integrate and graph $I$ vs $b$ the following integral (eq. 24 in this paper) in wolfram mathematica $$ I = \int_{2}^{\infty} \frac{g_i^3 \mathcal{K}_t \mathrm{~d} r}{r^2\left|\mathcal{K}...
Soliton-104's user avatar
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Find an instance satisfying equation

I have the following equation with two variables xi and nu. ...
Dotman's user avatar
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1 answer
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Solving system of first order PDEs

I am trying to solve the 1st order PDE system \begin{align} \xi_u^2+\eta_u^2&= \left(1+\frac{\xi^2+\eta^2}{4} \right)^2\\ \xi_v^2+\eta_v^2&=\left(1+\frac{\xi^2+\eta^2}{4} \right)^2 \end{align} ...
Daniel Castro's user avatar
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Galactic rotation speed and density research

Rotation speed of Milky Way looks like this until about 25 kpc I know the following points to describe this curve ...
Rémy Galli's user avatar
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Attempt to find a solution (out of potentially many) to a system of equations with FindInstance runs forever or crashes

I have a system of equations that in principle should have a solution (I would think not a unique one), which I want to solve. I am not interested in all solutions; I just want to locate one, assuming ...
AG1123's user avatar
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1 answer
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Minimization of an implicitly specified function

exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility I ...
Mam Mam's user avatar
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1 vote
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How to calculate and plot this integral? [closed]

Any help to integrate this equation: $$ \begin{eqnarray} p(k,q)&=&-16 H^2 q^2\int_{q_a}^q \int_{q_a}^q \frac{1}{\sqrt{H^2-k_1{^2}}}\sinh(\sqrt{H^2-k_1{^2}}(q-b))\frac{1}{H b} \...
Dr. phy's user avatar
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Training a neural network for solving PDEs and doing some predictions [closed]

I have been following the discussions presented in Teaching neural networks regarding the use of neural networks for solving PDEs. In their second example, they adjust the coefficient of a 1D heat PDE ...
Fazlollah's user avatar
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2 votes
2 answers
102 views

NDSolve of a non-linear ODE

I am trying to solve the following non-linear ODE numerically: ...
Zazu's user avatar
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74 views

Plotting complex roots in complex plane

I want to visualize the spectra (roots) of a quasipolynomial in Mathematica, for example: $$f(x) = x^2+x e^{-x}.$$ I know that it works nicely in MATLAB with the extended library, but I want to try it ...
Martin Strmiska's user avatar
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91 views

Why doesn't NMinimize work with NSolve?

Why does NMinimize throw the error and how to fix it? ...
Mam Mam's user avatar
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2 votes
1 answer
52 views

Event control in delay differential equations

A delay-differential system for variables {y[t],z[t]} is defined by time-lag w {y'[t] == (r (1 - y[t] - z[t]) - 1) y[t], z'[t] == (y[t] - y[t - w])}; The ...
DavidG's user avatar
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3 votes
1 answer
166 views

Numerical solution of the Richards' equation

I am trying to solve Richards' equation to model fluid flow in soil. The governing partial differential equation, initial condition, and boundary conditions are: The analytical solution of the ...
Tayfun's user avatar
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2 answers
100 views

Why can't NSolve find values that FindInstance can?

I am trying to solve for \[Epsilon], given three input paramters n, x and ...
Dotman's user avatar
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3 votes
1 answer
130 views

Solve Differential Equation Numerically

I investigated my system and encountered differential equation such as $y''(x) = e^{y(x)}-e^{-2y(x)}-e^{y(x)-y(x+d)}$, where $d$ is a constant. The boundary condition is $y'(0) = 30$ $y'(\infty)=0$. I ...
이영규's user avatar
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1 answer
57 views

`FindMinimum` can't evaluate `Nearest` numerically

I'm trying to use Nearest as a function to minimize over: a toy example is ...
Adam's user avatar
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1 vote
1 answer
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A code for producing system of equations for central difference method

I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ numerically over the interval $[0,1].$ Now using central difference method I arrived at the equations of the type $$ y_k = \...
Learner's user avatar
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Extend the code for more variables (at least 100)

I have this code (not in best shape) for a problem in 3 variables. It does the job. The problem is I want to extend this to more number of variables around 100 at least. It is very painful to extend ...
Learner's user avatar
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1 vote
1 answer
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What are some ways to speed up calculations

Below is the code for calculating the eigenfunctions and eigenvalues of the following system: $HC[u(\rho,z)]=-\frac{1}{2}\Delta u(\rho,z)-\frac{1}{\sqrt{\rho^2+z^2}}u(\rho,z)+\frac{B^2}{8}\rho^2 u(\...
Mam Mam's user avatar
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0 votes
0 answers
66 views

NSolve can't solve a system of 2 equations with 2 unknowns

I've been trying to solve a system of 2 equations with 2 unknowns using NSolve. But It's been too slow. I waited for more then an hour without any results. The code is: ...
Alen's user avatar
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2 votes
2 answers
120 views

Using ParallelTable for assignment

...
Mam Mam's user avatar
  • 1,753
5 votes
1 answer
183 views

Numerically finding a curve that satisfies an underdetermined set of equations

I am trying to determine a phase diagram along the lines of Fig 3. or Fig 4. of this pubilcation. The curves plotted are binodals and are determined by the conditions of equality of chemical ...
jcp's user avatar
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0 votes
1 answer
54 views

NMinimze cant find points that satisfy constraints

NMinimize cant find solutions for a function which clearly has one. Setting a working precision resulted in some output, however with error messages about tolerance and precision. Heres my code. The ...
Dotman's user avatar
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1 vote
0 answers
65 views

Numerical Error using compile

I'm trying to compile a function and I'm running into the following error CompiledFunction::cfne : Numerical error encountered; proceeding with uncompiled evaluation. I think I have succeeded in ...
Dotman's user avatar
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1 vote
2 answers
62 views

NDSolve for Coupled ODE with parameters

Here I solved sys1 using NDSolve for the parameter m. I want to solve sys2 using NDSolve. But in sys2 I have a term consisting of the derivative of the solution obtained from sys1. I am stuck on how ...
Dr. B. Mallick's user avatar
0 votes
1 answer
110 views

Performance improvements using Table and Compile

I'm converting a code from MatLab to Mathematica. It takes MatLab less than a second to compute it while its more than ten minutes in Mathematica. I was hoping to improve the performance. Here's a ...
Dotman's user avatar
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0 answers
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Dealing with Precision Issues in FindRoot for Complex Equations

I'm currently working on a Mathematica code that involves using the FindRoot function to find the poles of the scattering matrix in an one dimentional potetial well and for that, I need to find the ...
Eduardo Soares's user avatar
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2 answers
96 views

Finding the Minimum of a Four-Variable Function

Greetings esteemed colleagues. I had previously posted regarding the minimisation of a function using Mathematica, and colleagues were kind enough to provide some useful suggestions that proved quite ...
Hooman Puyandeh's user avatar
-1 votes
2 answers
439 views

Calculating a limit using Wolfram cloud or otherwise

Using Wolfram cloud or otherwise, I need to show $$\lim_{n\to\infty} \frac{n\ 4^{2n}}{e^{2n}}\ \left\{\binom{2n}{n} d_{2n}a_n\right\}\leq \frac{3}{4}$$ where $$a_n:= -\sum_{j=0}^n\binom nj^2(2(H_{n-j}-...
Max's user avatar
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1 vote
2 answers
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NDSolve "Coupled differential equation"

I am trying to solve the given coupled differential equation using NDsolve. $$ \begin{array}{c} n''(r)+\frac{n'(r) T'(r)}{T(r)}+\frac{n'(r)}{r}+\frac{n(r) T''(r)}{T(...
Shalu Rani's user avatar
8 votes
1 answer
752 views

To Chop or not to Chop

If I run the command ResourceFunction[ "GlobalMaxima"][{x*y + 2*y*z + 6*x, x^2 + y^2 + z^2 == 36}, {x, y, z}] This returns a closed form solution of ...
Moo's user avatar
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6 votes
1 answer
156 views

Result of numerical computation representing a real physical quantity still contains a small imaginary components [closed]

I have been grappling with a physics calculation pertaining to thin film optics. I have been endeavouring to use transfer matrix calculations to determine optical reflectance. Attached below is the ...
Hooman Puyandeh's user avatar
4 votes
1 answer
111 views

FindRoot error in NDSolve

I have two coupled differential equations as follows $$ \frac{\partial }{\partial x}U(x,y) =2V(x,y), $$ $$ \frac{\partial }{\partial y}V(x,y) =V(x,y)U(x,y)+1, $$ with ...
A.D's user avatar
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1 answer
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Why do the eigenvalues periodically change with successive increase in the consideration region?

When finding the eigenvalues and eigenfunctions of the system Hc[r, z] using NDEigensystem, the following issue arises: When ...
Mam Mam's user avatar
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0 votes
1 answer
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How could a function in a cylindrical coordinate system be plotted? [duplicate]

Below is the code for finding the eigenfunctions and eigenvalues of a particle in the Coulomb field using NDEigensystem. The problem is solved in cylindrical coordinates ($\rho,\theta,z$; $\rho \in [0,...
Mam Mam's user avatar
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5 votes
2 answers
154 views

Numerical integration of a list

I have a list, p, obtained by a complex numerical procedure. Its element has the structure: {k,fi,z}. Below I give a simplified ...
Alexei Boulbitch's user avatar
3 votes
3 answers
210 views

Solving a one-dimensional free-boundary problem with a singular boundary condition

Addendum (orginial question below). Thank you for the responses! After thinking some more about this problem, and thanks to @bbgodfreys helpful comment, I realised that the problem as posted below is ...
Anthony's user avatar
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