Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
2,056 questions
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NIntegrate on a solution of a matrix ODE
I've seen similar questions on this site but somehow the solutions there didn't manage to solve my specific problem.
I have a function mat1 that takes a square $n \times n$ matrix G, and some final ...
3
votes
0answers
26 views
Plot BV functions with singular derivatives in multiple space dimension
In 1-dimensional setting, two key examples of $BV$ functions (of bounded variation) $u: \mathbb R \to \mathbb R$ are the Heaviside function, whose derivative is the Dirac delta concentrated at $0$. It ...
4
votes
2answers
342 views
How to evaluate this function?
I’m trying to evaluate
y[t] = InverseFunction[ NIntegrate[Sqrt[2]/( -8+Exp[y]+2Exp[-y]), {y,0,t}]]
Some of the problems I’m facing, is that i’d like to get the ...
5
votes
1answer
177 views
+50
Numerical methods to solve a continuity equation
What numerical methods can be used to study the initial value problem for the continuity equation where $ u = u(t, x) $
$$
u_t + \nabla\cdot(\boldsymbol b u) = 0, \qquad t \in [0,T], \quad x=(x_1,x_2)...
3
votes
0answers
130 views
Boundary conditions are not satisfied with NDSolve
I want to study the time evolution of a small perturbation around the static solution of the following Wave Equation
$$
-\partial_t^2 v(t,r) + \partial_r^2v(t,r) + \frac{2}{r}\partial_r v(t,r) = \...
3
votes
3answers
77 views
Evaluating the error function by integrating $ \mathrm e^{−t^2} $ with Simpson's rule
I am trying to evaluate an error function with Simpson's rule because there is no other way to integrate it. The function is
$$
{\rm erf}(x) = \frac{2}{\sqrt π}\int_0^x \mathrm e^{−t^2}\, \mathrm dt
...
1
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0answers
25 views
Speeding up solving many coupled non-linear differential equations
I am currently working on a project that involves solving many coupled non-linear ODEs$^*$ I am using NDSolveValue and the time it takes to solve everything is (understandably) slow. But I was ...
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0answers
22 views
Integrating System of ODE's
I'm trying to integrate the system
$$\frac{d}{d z} \left[ \begin{array}{l}{\hat{a}} \\ {\hat{b}}\end{array}\right]=\frac{i \omega}{\overline{c}} \left[ \begin{array}{cc}{\left(\Delta_{l}^{(+)}-1\...
0
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1answer
45 views
Solving and Plotting an integral function
I am new in the use of Mathematica, so please forgive me..
I want to integrate and plot the following integral function:
$F(x)=\displaystyle\int_x^\infty\dfrac{t\sqrt{t^2-x^2}}{e^t-1}\text{d}t$:
...
0
votes
2answers
81 views
How to plot: $\int - \frac {W(-\ln x)}{\ln x} dx$? [closed]
How would we plot: $$\int - \frac {W(-\ln x)}{\ln x} dx$$
Where $W$ is the Lambert W function?
8
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0answers
152 views
+350
Solving the 2D Schrödinger equation with eigensystem, then verifying orthonormality of eigenfunctions with NIntegrate
I am solving the time-independent 2D Schrödinger equation for an interacting electron and hole in the case of anisotropic electron and hole masses, where the interaction is described a modified form ...
0
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1answer
89 views
Numerically solve delay ODE
I am trying to numerically solve a simple delay ODE in mma for the first time. I think this is likely a simple fix.
I first tried to solve system as ordinary differential equation system for up to 𝑡...
4
votes
2answers
147 views
Can I obtain more precise integration of highly oscillating integral?
I would like to numerically integrate precisely,
$$ \frac{1}{2 \pi r^{n}}\int_0^{2\pi} e^{-n i t}C(t)dt$$
with $C(t)$ a single-cycled branch of the function $w(z)$ given by the implicit expression
...
0
votes
1answer
65 views
Integral doesn't evaluate as it must be! [closed]
i have this integral it must result in all constant values and the value of the integral its self which is Zeta[2/3] it can be done.
...
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0answers
24 views
Using `Integrate` and or `FourierTransform`
I have some general questions about Integrate and FourierTransform. Firstly with ...
0
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1answer
54 views
Speeding up double NIntegrate
I am looking to speed up an integral of the type
$$
I(\omega,k,\mu,a,T,\eta) = \int_{-1}^1dx \int_0^{\infty}dq \,\frac{N_F(\sqrt{k^2+q^2+2kqx}-\mu)q^2f(k,q,x)}{(k^2+q^2+2kqx)^{3/2}(\omega+i\eta-q-a\...
0
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1answer
60 views
Parallelise numerical integral for contour plot
I have the following integral that I would like to evaluate:
...
0
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0answers
68 views
Using NDSolve to obtain solution
I am trying to solve the following ordinary differential equation but not getting result. Please help. Thanks
My code is
...
1
vote
1answer
60 views
Plotting 90% confidence ellipses for a gaussian pdf with small variances
Mathematica noob here, and I'm having some issues plotting 90% confidence ellipses of a small-variance 2D Gaussian PDF. I have it working perfectly fine for larger covariance matrices, but absolutely ...
0
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0answers
42 views
How can I speed up my code finding the parameter which yields zero determinant for increasingly larger matrices?
I build a square matrix with matrix elements dependent on the parameter x. I need to find all values of x within a reasonable ...
0
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0answers
37 views
NDSolve::ndsz: At t == -96804.6, step size is effectively zero; singularity or stiff system suspected
I am trying to solve these equations but couldn't figure out how to solve the NDSolve::ndsz error.
...
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0answers
42 views
Unable to numerically integrate a function I have defined
I am working with a polynomial and wish to integrate over one of it's branch surfaces with high precision.
The function is:
$$ -z^2 + z^3 + w (-4 z + 3 z^2) + w^3 (-2 + 8 z + 4 z^2 - 4 z^3) + w^2 (-...
2
votes
1answer
117 views
Numerical solution using RK4 to solve nonlinear ODE?
I am trying to use the Runge-Kutta 4 method to solve the nonlinear ODE, using the following Mathematica code:
...
2
votes
4answers
217 views
Integrating a list of values
The data given here
data = Table[Clip[Sin[x], {0, 1}], {x, 0, 2 \[Pi], 0.1}]
generates the following curve
ListPlot[data]
...
1
vote
1answer
69 views
Integrating only over positive values of an oscillating function
I have the following oscillatory function of time (it looks too lengthy!)
...
0
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0answers
41 views
How to NIntegrate a result derived from NDSolve?
I have the following code. My requirements are:
I want dp at y = h1 for different values of the parameter ...
2
votes
0answers
59 views
Solving 2d non-linear PDE with singular sources numerically [closed]
I would like to hear some suggestions on how to numerically solve a 4d Poisson equation with two singular sources, which can be brought to the following form (thanks to symmetries)
\begin{equation}
\...
3
votes
3answers
788 views
Solving system of ODEs with extra parameter
I would like to solve a $2\times 2$ system of the form
$$\frac{d}{d\theta}T=TA,\quad T(0)=Id$$
where $\theta$ is real and $A$ is of the form
$$A=\begin{pmatrix} 0 & \frac{e^{-i \theta}}{\lambda}\\ ...
0
votes
0answers
36 views
How to solve this error in numerical integration?
I am trying to integrate a function numerically and I get an error that I do not understand. The error is :
NIntegrate::slwcon : Numerical integration converging too slowly; suspect one of the ...
0
votes
2answers
88 views
Plotting a parametric solution from NDSolve
Im trying to animate multiple points around multiple parametric plots which depicts orbital motion of body around a planet. Initial conditons are;
...
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0answers
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1answer
63 views
Why is my integral not being evaluated?
I am trying to integrate a function Gamma, but the output returns the input. I have the following code:
...
8
votes
1answer
423 views
Ways to speed up user implemented RK4
So, I've implemented RK4, and I'm wondering what I can do to make it more efficient? What I've got so far is below. I wish to still record all steps. I think ...
2
votes
2answers
58 views
0
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1answer
119 views
Plotting elliptical orbits using Verlet method
I'm looking to solve a 2 body system consisting of the Earth and a body of mass in orbit.
I'm using the Verlet method to numerically integrate Newton's equation of motion in order to plot an ...
4
votes
2answers
266 views
NIntegrate: How can I solve this integral numerically? NIntegrate fails while Integrate works
I know the exact solution of the principal value of this integral is equal to zero:
$\int_{-1}^{1}\int_{-1}^{1}\frac{x^2}{\sqrt{1-x^2}}\frac{\sqrt{1-y^2}}{y-x}dydx=0$
doing:
...
0
votes
1answer
54 views
Complex number as the result of an integral [closed]
My question has been asked before by other members, however, I didn't find the answer to their question helpful in my case.
I'm doing a simple numerical integral with real numbers in mathematica, but ...
0
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1answer
109 views
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0answers
53 views
Cannot find starting value for variable
I am trying to numerically solve and plot two coupled first-order differential equations using ParametricNDSolve over the region $(0,a)$ where $a$ is the parameter.
...
0
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0answers
60 views
Approximate/estimate the ratio of two multidimensional constrained integrals
I have a hypothesis that a certain "qubit-qutrit separability probability" should assume the value $\frac{5}{3} \left(112 \pi ^2-1105\right) \approx 0.659488$. In its initial formulation, this is a ...
2
votes
2answers
132 views
What is the fastest way of doing one integral in Mathematica?
I want to compute the following numerical integral in Mathematica
$\int_0^L dy \int_0^y d \bar{y} f(y,\bar{y}),$
where $f(y,\bar{y})$ is a very complicated function.
I show my code below where the ...
0
votes
2answers
52 views
Numerically integrate complex valued function of a real variable and a complex variable
I need to numerically integrate a complex valued function of a real variable and a complex variable by the real variable. My integral:
$$ \int^1_{-1}\frac{e^{ix}}{x-z}dx ~~~\text{where} ~~x \in \...
2
votes
1answer
67 views
NDSolve solution plugged back into ODE quickly diverges
I have the following ODE with complex $\omega$:
$\qquad f(r)\frac{d}{dr}(f(r)\frac{dR}{dr})+(\omega^2-f(r)(\frac{1}{r^2}+\mu^2))R(r)=0,$
and with $f(r)=1-2/r$. I want to solve it starting at $r=2$ ...
2
votes
1answer
67 views
How do I divide an integral into parts and sum the total?
I have an exercise looking like this: Analyze the integral $4\int_{0}^{1} \sqrt{1-x^2} \, \mathrm{d} x$ numerically by deviding the interval ${]0,1[}$ into three equal parts, then summarize the ...
1
vote
1answer
87 views
Conditional evaluation: black hole cross section
I'm trying to calculate the collision cross section of black holes, more precisely, I want the critical impact parameter $b_{\text{crit}}$ for a given initial velocity $v$ such that, at this speed, ...
0
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0answers
67 views
Diverging solution to radial equation
I want to solve a seemingly simple eigenvalue problem. I have a fixed set of boundary conditions given and want to change the complex parameter omega in to minimize exponentially falling solutions for ...
3
votes
2answers
95 views
How to solve these ODEs using NDSolve?
I have six odes and I cannot use DSolve. So I tried NDSolve. But it says there may be some errors.The code is such like this:
...
6
votes
1answer
153 views
Maxwell construction problem with FindRoot
A Maxwell construction is just an integral of area and then solving for a root to find vapor pressure.
This must be exactly the same value as where the Gibbs energy plot crosses at a point. I found ...
