Questions tagged [numerics]
Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
2,234
questions
7
votes
3
answers
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NSolve uses all CPU resources
Is it default setting of NSolve that it uses all my four cores of CPU?
Be aware that the following code made my computer non-respondent for about 18 seconds till it ...
- 21.3k
3
votes
1
answer
145
views
Using NDSolve to solve the PDEs and their reduced ODEs yields inconsistent results
I am working with a system of coupled PDEs:
\begin{align}
\partial_tP_x(t,x)&=(\omega_0+\gamma gx)P_y(t,x)-P_x(t,x)/T_2+D\partial_x^2P_x(t,x)\\
\partial_tP_y(t,x)&=-(\omega_0+\gamma gx)P_x(t,x)...
- 451
1
vote
1
answer
60
views
1
vote
0
answers
46
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Entropy Production Rates
I am trying to reproduce the results shown in Fig. 2(a) of the paper https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.6.033037 to calculate entropy production rates in a cavity ...
- 11
1
vote
1
answer
115
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Is it possible to make an ODE-based system component that can be used repeatedly?
The background to my probelm:
The problem I want to address is the seismic response of a bridge after installing dampers. The kc component here refers to the ...
- 1,467
2
votes
1
answer
143
views
NSum result quite different from Sum. Euler Maclaurin won‘t work!
I have just computed this finite sum:
N[Sum[Sin[1000003451/k], {k, 1, 1000}], 100]
And the result is:
...
- 21
0
votes
0
answers
45
views
How to solve numerically a fourth order BVP having a Boundary condition at Limit Approaches to 0
I have the following fourth order BVP (pde):
$\frac{1}{4}f_{yyt}+H^{4}(ff_{yyy}-f_{y}f_{yy})=\frac{1}{H^{2}R}(yf_{yyy}+2f_{yy})$
with boundary conditions:
$f(0,t)=0$, $f(1,t)=0$, $f_{y}(1,t)=-\frac{\...
- 83
0
votes
0
answers
74
views
Second derivative from dataset or graph
I have a graph obtained from the eigenvalues of a matrix. I want the second derivative of each line (there are 3 independent curves in the graph) in specific ranges. Could you please help me?
One way ...
- 41
11
votes
1
answer
352
views
How to get inverse matrix for large size matrix in Mathematica?
Solutions to Hundred-dollar, Hundred-digit Challenge problems can be found easily:
Mathematica (MathWorld Notebook)
Python
I'm trying to solve the 7th problem:
Let A be the 20000×20000 matrix whose ...
- 1,947
2
votes
2
answers
84
views
0
votes
1
answer
25
views
`NMinimize` provides wrong answer when `WorkingPrecision` is specified
I'm trying to use NMinimize to solve the 4th question of Hundred-dollar, Hundred-digit Challenge problems
What is the global minimum of the function
$\exp(\sin(50x)...
- 2,255
0
votes
0
answers
58
views
How to evaluate Ginsh in Plot3D
I have a function F[x,y] containing multiple polylogarithms $G$ that can be evaluated numerically via GiNaC within the command Ginsh.
If say (toy example),
...
- 510
4
votes
0
answers
176
views
Issues in Reproducing Rippling Instability of Graphene using Mathematica from Physical Review B 101, 235428 (2020)
I'm attempting to reproduce the numerical model of the rippling instability of graphene as described in the paper "Physical Review B 101, 235428 (2020)" using Mathematica. Specifically, I'm ...
- 466
4
votes
1
answer
298
views
How to port Matlab/Python's multivariate FoxH implementation in Mathematica?
Ref code
MATLAB
Python
My implementation
Are there some mistakes in my Mathematica code? Any help would be greatly appreciated.
Attempt Version 1 (❌)
...
- 1,947
2
votes
1
answer
81
views
Generating numerical value for skin friction coefficient
I am trying to generate the numerical values for the skin friction coefficient by using the value of the parameter in the procedure of the attached code. When I run the attached Mathematica sheet code,...
3
votes
1
answer
121
views
Computing norm of a matrix with positive entries
Is there anything in Mathematica that can help me compute norm of a matrix with non-negative entries faster than Norm? Approach below works for ...
- 8,041
0
votes
0
answers
78
views
Numerical values of physical quantities for using in the table of research paper
I am using method of lines for numerical solution of PDEs in mathematica. I have want to find the different numerical values for physical quantities I.e. skin friction coefficient, Nusselt number, and ...
1
vote
2
answers
117
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NDsolve does not solve equation
I have a question for system of ordinary differential equations, because Mathematica does not give the solution. To be more specific, it does not give any sign that there is some problem. There is the ...
2
votes
1
answer
89
views
How to numerically integrate the following expression?
Let
fK[T_, D_, t_, H_] :=
Integrate[(r - t)^(H - 1/2), {r, T, T + D}]
fI[T_, D_, s_, u_, H_] :=
Integrate[((r - u) (r - s))^(H - 1/2), {r, T, T + D}]
.
I ...
- 155
1
vote
1
answer
70
views
Mathematica can't handle expressions with Bessel functions in the limit of a large argument [duplicate]
Consider the following function:
...
- 5,923
2
votes
2
answers
129
views
2
votes
2
answers
218
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Numerical derivative of numerical function
I am trying to calculate the derivative of a numerically defined Hamiltonian. This is a minimal working example (on a simple example):
...
- 133
0
votes
0
answers
85
views
Chebyshev Subdomains
The following piece of code creates a grid subdivided into equally spaced Chebyshev subdomains as well as the corresponding differentiation matrix. In this example, we have four subdomains, each with ...
- 535
0
votes
0
answers
51
views
Speed up the evaluation process
I am writing a code to simulate some spins. Following is the main part of the code:
...
- 552
3
votes
3
answers
172
views
Looking for the asymptotic solution of $x \log (x)-(x+n) \log (x-n)=0$
Working this problem on Mathematics Stack Exchange, I very quickly obtained as an estimate of $x$ solution of
$$x \log (x)-(x+n) \log (x-n)=0$$
$$x_n^{(0)}=n+\sqrt n+\frac 14 \log(n)+\frac 12 \tag 1$$
...
- 1,001
6
votes
3
answers
452
views
Why do I get different results for the products of two identical expressions?
I have two expressions with the Gamma function that are identical:
...
- 3,169
0
votes
2
answers
104
views
How to Solve a Piecewise PDE System in Mathematica?
I'm working on a problem involving the transverse vibration of a piecewise beam system. The system consists of two segments with different properties (length, Young's modulus, second moment of area, ...
- 103
2
votes
0
answers
91
views
Demonstration of different Gaussian quadrature
I am doing demonstration about Gaussian quadrature.
Any supplementation would be greatly appreciated.
Related:
Gauss-Legendre and Gauss-Jacobi quadrature, in MATLAB
My question is:
The answer ...
- 1,947
1
vote
1
answer
112
views
Challenges with High-Order Boundary Conditions in PDEs for Beam Vibration Analysis in Mathematica
I am trying to solve a problem involving the longitudinal vibration of a beam in Mathematica. The beam is fixed at the left end and has a concentrated mass at the right end. The system is subjected to ...
- 103
0
votes
0
answers
63
views
How to efficiently find the series of quasi-normal frequencies using FindRoot?
I want to use FindRoot reproducing the following result in the table 1 of the article "Scalar gravitational perturbations and quasinormal modes in the five-dimensional Schwarzschild black ...
- 51
2
votes
1
answer
191
views
Any ideas on how to use NDSolve to solve this nonlinear 2nd order ODE
I can't get to work this code to solve a nonlinear second order boundary value problem.
...
- 333
1
vote
1
answer
93
views
When using FindFit to fit a large dataset with multiple sine functions, a step size error occur
My dataset looks like
datatandA = Import["dataForQuestionFindFit20240528.csv"];
ListPlot[datatandA]
and the corresponding FFT spectrum looks like
...
- 451
5
votes
3
answers
234
views
Singularity or stiff system suspected in ODE that shouldn't have a singularity in the solution range
I am trying to numerically solve the following ODE where I know the value at p[1000]:
...
- 5,117
6
votes
3
answers
442
views
How many solutions does this system have?
Let us consider the system of two transcendental equations ...
- 27.8k
2
votes
0
answers
90
views
How to push the performance of this compiled function
I have the function optvals solving for two variables. For the given example of variables, I need the program to run atmost in a millisecond.
The main part of the ...
- 496
1
vote
1
answer
90
views
How to speed up generating and filtering large lists of numbers?
I have the following code where I brute force search for two variables.
list gives a list of 3 dimensional vectors, say {x,y,z}. ...
- 496
1
vote
1
answer
370
views
Gillespie (stochastic simulation) algorithm
I want to apply the Gillespie algorithm to a set of reactions. First, I run the source code presented here, and then run my model:
...
user96206
0
votes
0
answers
33
views
1
vote
0
answers
67
views
Numerically solving coupled 2rd ODE with tiny numbers
I am solving the initial value problem of two coupled ODEs numerically.
The equations are
...
- 31
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vote
1
answer
49
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1
vote
2
answers
99
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1
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0
answers
75
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Problems with implementation of subresultant pseudo-remainder sequence in Sturm's theorem
I've implemented the subresultant pseudo-remainder sequences ( https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Pseudo-remainder_sequences ) as described in Wikipedia. However, when ...
- 111
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votes
1
answer
44
views
ContourPlot does not draw intersection point and draws ragged plots [closed]
I have the following implicit equation:
$$
M^{-2\frac{\gamma-1}{\gamma+1}}(r)+\frac{\gamma-1}{2}M^{\frac{4}{\gamma+1}}(r) = \frac{g(r)}{g_0}\left( M_0^{-2\frac{\gamma-1}{\gamma+1}}+\frac{\gamma-1}{2}...
- 4,016
0
votes
0
answers
33
views
Making NSum faster with higher precision and accuracy
I have the following code that I want to run to obtain a cumulative list out of various values of s1=3 to s1=10 (say) for the ...
- 411
0
votes
3
answers
131
views
Properly define function from outcome of NSolve and FindRoot
We have the function $\gamma(u,v)$ defined implicitly as the solution of
\begin{align}
\sin\gamma(u,v)=g\left(u-v\cos\gamma(u,v) \right),
\end{align}
being $g$ a given function. I can solve for $\...
- 609
4
votes
3
answers
261
views
How to make Mathematica plot for a very small region?
I have the following data that I would like to plot using ListPlot.
...
- 411
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vote
0
answers
74
views
How can I ask Mathematica to give the explicit real form of the given function?
In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, ...
- 195
0
votes
0
answers
52
views
Ising Model Simulation Increase Efficiency
I implemented a 2d simulation of Ising Model for zero external magnetic field. Below you can find the function I wrote to calculate the energy (periodic conditions)
...
0
votes
1
answer
61
views
Tan function problem [closed]
Why does the Tan function give values for 0, and 30 Degree, but not for the others? Strange behavior?
In[16]:= Tan[0 Degree]
Out[16]= 0
In[23]:= Tan[10 Degree]
Out[23]= Tan[10 °]
In[24]:= Tan[20 ...
- 199
1
vote
0
answers
61
views
Adapt Code to Solve Fractional-Order System Delay Differential Equations- Chen System
Dynamics of fractional-ordered Chen system with delay
I have tried to modify this code
...
- 11