Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
2,850
questions
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Passing Product function through NIntegrate?
I have a set of intervals, Times1, that I have calculated using the following code. This code works well on its own.
...
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1
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34 views
2
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1answer
91 views
Calculating Residue with NIntegrate fails
Trying to answer this interesting question Principal value from two different axis I observed a problem using Nintegrate:
The function ...
3
votes
1answer
103 views
Principal value from two different axis
I have an integral where its limits of integration is from the imaginary axis to the real axis, specifically,
$$\int_{\pi i/2}^\infty \frac{dp}{\sinh(p/2) \sqrt{\cosh(p)}}$$
I want to evaluate this ...
1
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0answers
101 views
Yet another slow plot involving numerical integration
Well, after reading a lot about how plotting expressions involving NIntegrate can take a lot of time, and how to overcome this issue with ...
1
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1answer
65 views
Contour integral does not converge
I have this integral where I want to evaluate it on the imaginary axis. However, it says that it does not converge even though I have introduced a small indentation $a$,
...
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0answers
36 views
How can I isolate a specific variable to one side in an equation?
Firstly, I will integrate the equation using Simpson's 3/8 Rule since it is quite long to do analytically. All the variables
(x, y, r, n, ps, k) are unknowns. I want to make r as the subject.
I tried ...
1
vote
1answer
126 views
Contour integral around complex plane
I have this integral where it is singular at the points $p=\{0,\pi i\}$, where the solid contour is given in the image below. My goal is to find the integral in the range $[0,\infty]$ (the horizontal ...
2
votes
1answer
46 views
Passing a Piecewise function of NIntegrate through NIntegrate?
I am trying to pass a piecewise numerical integral (function1) through another numerical integral (function2). When I try this, however, I receive an error that says "t = T is not a valid limit ...
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74 views
Numerically integrating interpolating function whose initial conditions vary?
I am trying to numerically integrate--with respect to t0--an integrand (entitled function1 below) that involves an NDSolve interpolating function whose initial conditions are a function of t0. When I ...
1
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1answer
83 views
NIntegrate with variable in it
I would like to NIntegrate with a variable in the function. Later I will be series expanding it. Can it be done in Matehematica? I am getting errors for a sample ...
2
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1answer
195 views
How to calculate this integration accurately
I need to calculate this integration:
$\int_0^{2 \pi}\int_0^{2 \pi}\int_0^{2 \pi}\ F(x,y,z) $
which:
$F(x,y,z)=\left\{
\begin{array}{rcl}
f(x,y,z)^2 & & {0 \leq f(x,y,z)}\\
0 & &...
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35 views
High-dimensional second-order differential matrix equations
I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known:
$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$
where $q=[\dot{\...
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1answer
61 views
Highly oscillatory Integral over Airy function
I have to (numerically) integrate this function over all p from to get a function g(x):
...
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1answer
61 views
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What are the valid options for the “ParametricCaching” option in ParametricNDSolve?
I am using ParametricNDSolve as part of the calculation of an objective function for an optimization, so I am trying to strike a balance between memory usage and ...
1
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0answers
29 views
How to NSolve when an NIntegrate is involved?
I need to find the set of 3rd order polynomial coefficients that will give a bounded exponential function f(x) = Exp[ c0 + c1x + c2x^2 + c3*x^3] a set of specified 0th,1st,2nd,and 3rd order moments.
I ...
1
vote
1answer
82 views
Defining a region in Mathematica
I have two functions which are eigenvalues:
$$
E_+= a*x-\sqrt{(b-x^2-y^2)^2+d*(x^2+y^2)}$$
...and...
$$ E_-= a*x+\sqrt{(b-x^2-y^2)^2+d*(x^2+y^2)}.
$$
How do I define a region $\left|E_{\pm}\right|<...
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1answer
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NIntegrate over 2D region failed. Simple integrand. Complicated region
The integrand is simply a Gaussian curve over one of the variables
PDFTheta[the_] := PDF[ NormalDistribution [0, DeltaTheta/2], the]
The region of integration is ...
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0answers
40 views
Integrand that is divergent at some points
I have a function $f(x)$ where it has a singularity at the point $x=10$.
$$f(x) = \frac{-1}{g(x) \sqrt{1 - \frac{a^6 g(x)}{x^6 g(a)}}}, \qquad g(x) = 1 - \Big(\frac{x}{h}\Big)^4, \qquad a=13.128, \; h=...
4
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2answers
107 views
Obtain $\{h_1,h_2,\ldots\}$ from $\{f(0),f(1),f(2),\ldots\}$ with $f(s)=\sum_{i=1}^n \exp(-h_i s)h_i$
I need to obtain $\{h_1,h_2,\ldots\}$ when given $\{f(0),f(1),f(2),\ldots\}$ with $f$ defined as follows
$$f(s)=\sum_{i=1}^n \exp(-h_i s)h_i$$
We know that $h_i>0$. Is there a way to do this ...
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0answers
20 views
Nintegrate Using coordinates specified by a matrix
How to do a 3D Nintegrate over a function while specifying the co-ordinates to be used? I have the coordinates in a n*3 matrix and want integral to be performed over those points only.
2
votes
2answers
86 views
NIntegrate doesn't work on regional integration
I use FEM to solve a PDE in a spherical region and I want to integrate the result within half of the spherical region.
I wonder why NIntegrate doesn't work here. The integrant should not have ...
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0answers
128 views
How to solve this differential equation numerically?
I am solving a rather complex differential equation in 4d space plus time. Here is the Mathematica code to do this:
...
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1answer
91 views
NIntegrate and Integrate give different results [closed]
Good morning, I computed the following integral
...
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1answer
90 views
Mathematica residual miscalculation
I am trying to apply the residual theorem of Complex analysis for the calculation of an inverse Laplace operator. My function is the following:
...
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67 views
Four dimensional numerical integration
I am trying to perform the following Integral involving Bessel Functions as well as Heaviside Functions:
...
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1answer
45 views
NIntegrate not evaluating. “Interpolating Function” [closed]
I am trying to numerically evaluate an integral. I have a function to be integrated, ftbI[s,a] with undetermined variable(s) a. ...
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0answers
45 views
Numerically solve system of ODE
I have the initial problem for system of ODE, that I want to solve numerically with a given accuracy $\varepsilon$:
...
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2answers
92 views
Is there any way to speed up this Mathematica evaluation?
I am interested in evaluation of the following integral
...
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0answers
44 views
Instability in NIntegrate
I am solving the following equation with NIntegrate. However, the solution branches off at a certain time instance. When I increase the time step size, the instability occurs at larger time instant. ...
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43 views
“The integrand has evaluated to non-numerical values…” for only a _subset_ of the function domain?
What might cause NIntegrate to complain about the integrand evaluating to non-numerical values for only some subset of the function's domain?
I have a pretty complicated function whose (numerical) ...
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133 views
How can I speed up this pdf path integration calculation with a slow recursive function with 40^4 summed terms in each iteration?
I am writing a path integration code for a numerical approximation to a probability density function.
I essentially take some initial continuous probability density function p0 and then perform a ...
1
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1answer
97 views
Problem With NDSolve, Mathematica does not run [closed]
Hello everybody I was solving an exercise that its solution was the solution of a system of differential equations but when executing the command in mathematics this takes a long time and then the ...
6
votes
1answer
108 views
Defining mesh size for NDSolve
I want to see the effect of mesh size on the solution curves while simulating convection-diffusion - point sink via NDSolve FEM.
In the following code (ref also related to this post):
I'd like to know ...
0
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1answer
55 views
problem with NDSolve using RungeKutta
I'm having a problem with using NDSolve.
It might be a simple problem, and related to the method's parameters, yet I'm not sure how.
I have two deferential equations, and I'm trying to get the ...
4
votes
1answer
149 views
How can I speed up this Monte Carlo integration for the Stieltjes constant $\gamma_n$?
Pre-requisite Definition
Stieltjes constants ($\gamma_n$) are the constants that occur in the Laurent series expansion of the Riemann zeta function.
$${\displaystyle \zeta (s)={\frac {1}{s-1}}+\sum _{...
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1answer
87 views
Issues to compute and plot a function with some Fourier analysis
I'm currently in an internship and I have to construct a model that involve Fourier transform of 2 orbitals. My issue is that when I run the programm, the function evluateton non numerical values : &...
2
votes
1answer
93 views
NIntegrate fails to solve a double oscillatory integral
I need to compute the following integral:
...
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1answer
85 views
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1answer
138 views
How can I solve this system please?
I need to solve the following impulsive heat equation:
$$
\left\{\begin{array}{ll}
\partial_{t} \psi(x,t)-\partial_{xx} \psi(x,t)=0, & (x,t)\in (0,1) \times((0, 2) \backslash\{1\}) \\
\...
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0answers
39 views
What is the units of source term
This is a follow up to my previous question posted here,
I'm setting up a pde in 1D to simulate the convection-diffusion physics along with point sinks
...
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1answer
48 views
Nested usage of NIntegrate
I'm trying to compute an integral of f(x,y) such that an integration over "y" is performed inside the integral over "x". My trial is below:
<...
0
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1answer
108 views
plot multiple curves : solution obtained from NDSolve
I want to plot the solution obtained from NDSolve as a multicurve plot like shown in the
following sample image (image ref). Here, x1, x2 , x3, x4 .. are the solution computed at ...
1
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0answers
48 views
Closed form for integral with SinIntegral
MMA can't solve this integral:
$$\int_0^{\pi } \text{sinc}(x) \text{Si}(2 x) \, dx$$
The I use FourierSinTransform to find closed form,but I try a verify result is ...
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0answers
51 views
Strange results: Absolute value vs. square root of square in integral computations
Today I encountered a phenomenon in the free online version of WolframAlpha which looks to me like a bug. It would be great if someone could check whether the phenomenon also occurs when using ...
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0answers
41 views
WhenEvent with 2 conditions to stop integration
I have this code that does not even work for a single condition, say
...
5
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4answers
147 views
Are there any alternatives for NIntegrate to calculate the area for which $f(x,y)<0$?
I have this two-variable function
$$f(x,y)= (8 \cos (x+y)+7)\cos \left(\frac{x}{2}\right)+\cos \frac{x-2 y}{2}+2 \cos \left(\frac{3 x}{2}\right) $$
where $0<x,y<\pi$. I want to calculate ...
2
votes
1answer
67 views
Why does the integration of this symbolic matrix slow down after compilation?
There's a symbolic matrix as the following. Why does the integration of the symbolic matrix slow down after compilation? How to eliminate the error information in red? Thanks.
Note: The sample matrix ...
