Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
2,202
questions
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Non-linear differential equation with tricky variable dependence
My problem regards solving a differential equation and can be reduced to the problem of finding $f(x)$ such that
$\frac{df}{dx}=\frac{dh}{df}$, with $h(f)$ a known function.
I have this list of data,...
0
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0answers
27 views
Solving Integration with exponentials
I am trying to solve this integration :
Integrate[(1 - Exp[-a*x])* (1 - Exp[-b*x])*(1 - Exp[-c*x]), {x, 0, t}]
I get the result. But when I use the below ...
0
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0answers
51 views
Where is the numerical solving breaking down?
I am working with a set of three coupled reaction-diffusion PDEs, and for some parameter values I am getting some not so great solutions. I have been searching documentation and tutorials, and I have ...
2
votes
1answer
38 views
Solving numerically an equation with an integral
I am trying to solve the following equation numerically:
Equation to solve for $y$:
$$na(ay-y)^{n}\int_{ay}^{+\infty} \frac{(x-y)^{-n}}{x-ay}dx=b$$
with for example $a=4$, $n=1.25$ and $b=1.6$.
I ...
2
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0answers
146 views
+100
Finding local minima of an energy defined by integration
This question is also asked here and here.
I would like to reproduce the two solid curves in Fig. 1a of this paper. The total energy is given in Appendix A, and the curve is obtained by minimizing ...
4
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1answer
117 views
How to include conditional statements in NIntegrate?
I have a function g which is the result of another integrated function f. This function (f) ...
0
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0answers
62 views
How to solve this equation in Mathematica?
I wonder what is the best way to solve this equation in MA?
$$ y= \frac{\partial}{\partial x} ~ \frac{\partial}{\partial x^*} f $$
where y and ...
2
votes
1answer
55 views
Computing the definite integral of a fractional polynomial containing sin(x) and x^n
I need to compute the definite integral defined as $$\int_{-\infty }^{+\infty } \frac{\sin ({x_0}\, \omega )-\sin (x \omega )}{(\sin (x \omega )-\sin ({x_0}\, \omega ))^2+(x-{x_0})^2} \, dx\,.$$
When ...
2
votes
2answers
43 views
Integrating a function with Max function
I'm trying to evaluate the triple integral
$$\int_{0}^{1} \int_{0}^{1-x} \int_{0}^{1-\max(x,y)}1 dzdydx$$
in Mathematica. The code I'm using is simply
...
0
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0answers
69 views
Want help with handling error messages from NDSolve [closed]
I'm trying to solve a system of two differential equations with NDSolve and mathematica gives error.
I have functions in ...
0
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0answers
25 views
Help with NIntegrate with singularity and variable integration limit
I have a function of the type:
$$ F(x,z)= \int_{-\infty}^{\infty} dx' \int^{z}_{-\infty} dz' f(z,z',x,x')\frac{\partial g(z',x')}{\partial z'}$$
where the integration order may be interchanged. I ...
0
votes
2answers
29 views
NIntegrate user defined function
I have the the function
f[a_] := Module[{solution, ans, x}, solution = NSolve[x + a == 4];
I want to integrate it by writing
...
0
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0answers
34 views
How to stop NIntegrate if the integral appears to be smaller than certain value?
I have a number of integral to compute numerically. The values of some of them are small as those take NIntegrate very long to compute according to its internal goals.
Now, I care only about the ...
-1
votes
0answers
34 views
Gauss Quadrature Error in 2D [closed]
Could someone tell me what is the error when applying the Gauss Quadrature rule in 2 Dimensions?. I Know that for one dimension the error is
...
0
votes
0answers
40 views
How to resolve underflow occurrences?
I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve.
...
0
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2answers
98 views
Numerical resolution of non-linear coupled ODEs
I have problem with my code in Mathematica. I have introduced the set of coupled non-linear ODES. This is the resolution part:
...
0
votes
2answers
48 views
Can't solve for y in a fairly simple work done by magnetic field equation
The equations below are essentially calculations for a railgun-type mechanism (here is a good image description). I also drew an image using my own variables as definitions:
I assumed that ...
1
vote
1answer
51 views
Hybrid ODE simulation with very small parameters
I am trying to solve a Hybrid dynamical system using NDSolve and WhenEvent. I am able to simulate when the parameters are close ...
1
vote
1answer
77 views
About some hypergeometrical formulas for roots of trinomial and quadrinomial
Please correct my interpretation of formulas by Pietro Majer from post.
For equation $a=x+x^p$
one root is $x=a\sum\limits_{k=0}^{\infty}\frac{(-a)^{(p-1)k}}{(p-1)k+1} {{pk}\choose{k}}$
Wolfram ...
-1
votes
1answer
112 views
Can I numerically solve these equation in Mathematica? [closed]
I have this couple of equations :
$ \partial_\mu \partial^\mu z^i + G^{i\bar{p}} (\partial_j G_{k\bar{p}} ) \partial_\mu z^j \partial^\mu z^k + G^{i\bar{j}} (\partial_{\bar{j}} G_{k\bar{l}} ) \...
2
votes
1answer
72 views
Is it a mistake in the formula or inaccuracy in the calculations of numerical integration?
Formula for roots of trinomial $\displaystyle z^m-az^n-1$ with definite integration from paper Лахтинъ, “Выраженiе корней трехчленнаго алгебраическаго уравненiя посредствомъ опредѣленныхъ интеграловъ” ...
0
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0answers
63 views
Difficulty numerically integrating highly oscilliatory function
I have the following two integrals that I wish to numerically integrate. The function in each integral is the same. They have been split up since at t = 0 there's a singularity.
...
5
votes
2answers
174 views
How to count the number of function evaluations in NIntegrate
I expect the following code to count the number of function calls in NIntegrate.
...
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0answers
29 views
Moment-generating function of the log-normal distribution. A question about integration
Consider the probability density function $f(x)$ of the log-normal distribution with parameters $-0.1$ and $0.01$:
...
0
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0answers
28 views
NIntegrate fails to converge despite using attempting to use different methods
I have the following Green's function that I am trying to evaluate for several different values on a defined mesh. The mesh and Green's function is defined below. The mesh runs from values -w/2 to w/2....
0
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1answer
55 views
6
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1answer
377 views
Can NDSolve address spherical gravitational collapse?
As far as I know spherical gravitational collapse -of central importance to theoretical physics- is thought to be out of the scope of Wolfram Mathematica.
However there are cases, as in this article,...
5
votes
3answers
224 views
0
votes
1answer
71 views
DSolve returns unevaluated(I need a closed or numerical solution for this system and plot solution)
I am trying to find a solution to this system of differential equations but the program gives the same output without any messages. I would like help. Please find the Mathematica code posted here. a ...
2
votes
1answer
143 views
Double Numerical Integral - precision is not improving answer
Consider this two-dimensional integral
...
3
votes
1answer
135 views
Analytical form of 2d integrals relevant to graphene
This question is continuation of my previous post.
Alex Trounev was very helpful in fixing a crucial typo in the analytic solution known from the article "Density Dependent Exchange Contribution to ∂𝜇...
3
votes
1answer
63 views
Unexpected error when implementing FEM in MoL SpatialDiscretization
I cannot figure out why the following piece of code
...
4
votes
2answers
81 views
MoL: How to enforce Chebyshev–Gauss–Lobatto points in SpatialDiscretization?
In Mathematica documentation one is prompted to use a grid with points at the zeros of the Chebyshev polynomials so that Runge's phenomena arising from ...
2
votes
1answer
112 views
Elliptic integrals
In trying to reproduce results from one paper I stumbled upon a problem with definition of some elliptic integrals (this is my guess of what could be the problem).
I will first present in a ...
1
vote
1answer
23 views
Visualizing a multiple parameter integration
I'm really new to Mathematica and all the other answers to similar questions don't seem to help me. I have an integral I'd like to solve, and I'm having problems. My integral looks like this:
$\int_{...
1
vote
1answer
48 views
Elimination of numerical error in initial data
Elimination of numerical error in initial data can be crucial for its subsequent evolution.
In the following simple example
...
2
votes
1answer
43 views
TemporalDiscretization in MethodOfLines
When solving ODE's one can use options like MaxStepFraction to control the number of grid points.
When solving PDE's ...
6
votes
2answers
783 views
Integration of Interpolated function take an unacceptable amount of time
I have a simple integration which, when using an interpolation function, is taking too long to calculate:
...
1
vote
1answer
82 views
Solving system of PDEs with NDSolve
I am trying to solve a system of coupled PDEs with zero-flux boundary conditions on a large domain.
I have two problems:
1) Is there a possibility to use results of NDSolve as inititial conditions? ...
3
votes
1answer
91 views
Solving a stiff nonlinear ODE system
The system I am trying to solve is simple, but looks pretty stiff and I have unsuccessfully tried to solve it with StiffnessSwitching. It is the following one:
<...
2
votes
1answer
72 views
Evaluating the Poincaré section for Hénon-Heiles potential through Hénon Method
I must find a poincaré section of a Hénon-Heiles system as described in Hénon-Heiles 1964 paper.
The Hénon-Heiles Hamiltonian is the following,
$$
H = \frac{1}{2}(p_{1}^{2}+p_{2}^{2}+q_{1}^{2}+q_{2}^{...
8
votes
1answer
613 views
Correct way of simplifying the result of an integral
Many times Mathematica gives enormous results to simple problems. One uses the program more for trouble than for not knowing how to solve the problem.
As an ejemplo I present this integral that ...
2
votes
0answers
70 views
Solving 2D Integro-Differential equation numerically
The following problem was given to me by a friend, so I can't really guaranty that a solution exists, but if, I certainly can't find it myself...
Let us consider the following Integro-differential ...
0
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0answers
45 views
NDSolve 1/0 error
I'm having trouble to solve a differential equation with NDSolve. Does anyone knows how can I get rid of this problem?
...
0
votes
2answers
75 views
Getting an empty plot after plotting the solution of a differential equation
I am facing problem to plot this
...
5
votes
1answer
165 views
How to increase NDSolve accuracy for 2nd order ODE?
My attempt to NDSolve a 2nd order nonlinear ODE
...
1
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0answers
53 views
Computing a system of ordinary differential equations with initial condictions over a continuous range [on hold]
I have some questions about Mathematica programming and would appreciate if you could help me.
I want to solve a system of ordinary differential equations μ '[t] ...
1
vote
1answer
40 views
Plotting a function on the different axis
I've solved the DE:
$$a\cdot x(t)+b\cdot\ln\left(1+c\cdot x(t)\right)=-p\cdot x'(t)\tag1$$
Where $x(0)=k$
And I got the following solution:
$$t=\int_{x(t)}^k\frac{p}{a\cdot z+b\cdot\ln\left(1+c\...
0
votes
2answers
37 views
NDSolve: How to perform a reverse integration consistency check?
Let there be the following NDSolve code:
s = NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}]
I think it ...
0
votes
1answer
111 views
Verifying that an inequality has a finite limit
I am trying to verify the following inequality using Mathematica, but without any success.
$$
\lim_{a\rightarrow0^{+}}\frac{\intop_{0}^{1}e^{\frac{-30}{\sqrt[15]{a^{16}*\log\left(\frac{1}{x}\right)}}}...
