Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
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NIntegrate failed to converge to prescribed accuracy for integral contain Bessel function of first kind
I am new in Mathematica, I try to find the following numerical integral.
but I get the error message ( NIntegrate failed to converge to prescribed accuracy ...), I know that there is a divergence ...
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1
answer
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NIntegrate::nlim: * is not a valid limit of integration
The following numerical integral within a numerical integral:
...
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Why this integral is calculated incorrectly？
Input:
Integrate[1/y - Floor[1/y], {y, 0, 1}]
N[Integrate[1/y - Floor[1/y], {y, 0, 1}]]
Output:
Integrate[1/y - Floor[1/y], {y, 0, 1}]
0.418638
The above code is ...
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Mathematica vs other languages such as C or Python [closed]
I need your valuable opinion on a very controversial question regarding Mathematica versus other languages, in particular C or C++. For computation, analytical or numerical in physics or other areas, ...
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NDSolve error in Functional Delay Diff Eq
I'm trying to use Mathematica to study an equation that has an unusual dependence on past states, i.e. some kind of a Delay Diff Eq. For the sake of this post, we can say that the equation I would ...
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Mathematica or math question: why my own Monte Carlo gives different result from the Mathematica's one?
Consider some function of arguments x,y,z, where the latter have some domain of definition $\mathcal{R}$:
...
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Multi-NIntegral with a compiled function: Why not improved so much?
I want to compute the multi-dimensional integral by using NIntegral with the compiled function.
I have compiled an integrand function.
It made the computation time of the integrand about 100 times ...
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3
votes
2
answers
163
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Need help to speed up the Gaussian quadrature
I am trying to compute the $L_2$-norm of the solution $y(z,t)$ of a PDE with Gauss quadrature using the following code, where $z$ is space position and $t$ is time, then to construct it as a function ...
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Memory Allocation Error with Principal Value Integral
I'm getting a SystemException["MemoryAllocationFailure"] error with some arguments to S[x] in the following ...
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1
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71
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Numerical solution of differential equation with DiracDelta fit boundary condition at zero poorly
I need to solve: $x^2y''(x)+(2x+1)y'(x)-x^2\omega^2y(x)=\frac{-\omega^2\delta(x-x_0)}{4\pi},x\in[0,\infty)$ with boundary conditions:$y(0)=1,\ y(\infty)=0$ , $\omega$ is a function of this form: ...
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How to improve the integration accuracy without significant reduction in the speed?
Consider some distribution:
...
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Discrepancies in NDSolve Solution Between 4D and its Reduced 3D Counterpart
I have two systems, a 4D system and a 3D system. The 3D system is a reduction of the 4D system in such a way that:
...
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Why the output curve is not smooth?
tmr is the output funciton which is a complex integral, and afa is the variable. If gama is a real number, for example, gama=-410^(-29)(1 - Cos[6afa]), A2 and A3 can be infinity, and there will ...
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How to create and plot a function involving NIntegrate
I am interested in understanding the growth of the following function for $n\geq 2$
$$I(n) = \int_{0}^{1/2}\frac{ds}{s^{1-1/n}+(1-s)^{1-1/n}-1}.$$
I can explicitly compute $I(n)$ for various values of ...
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NDSolve for Fluid Flow - Monitor Residuals
I'm using NDSolve for fluid flow and would like to monitor the convergence of the solution more closely. I have a simple stationary case set up. NDSolve should return the solutions for u,v and p. ...
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Problem with parametric integral with variable bounds
d[p_, B_] := \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-B\), \(+B\)]\(Cos[
p\ x] \[DifferentialD]x\)\)
Plot[d[x, 2], {x, -10, 10}, PlotRange -> Full]
I ...
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Trouble plotting particle geodesic trajectory on wormhole embedding
I'm having tremendous trouble plotting geodesic trajectories on wormhole embedding. I'm attaching the article from which I am trying to re-create the trajectories (https://arxiv.org/pdf/1404.7210.pdf)....
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Crank-Nicolson solver for heat equation
My ultimate goal is to solve the 1D radial diffusion equation
$$\frac{\partial u(t,x)}{\partial x}=x^2\frac{\partial}{\partial x} \left(\frac{D(t)}{x^2} \frac{\partial u(t,x)}{\partial x } \right)$$ ...
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Attempt to code an Integro-Differential Equation Solver
I'm interested in constructing a code that is able to numerically integrate a function at discrete points in order to implement into a numerical solver for a set of Integro-Differential Equation. In ...
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1
answer
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Multiple Integration of a function defined for a list of arguments [closed]
I want to calculate, by Mathematica, the following integral of a function defined with a list of arguments.
$$\int_1^2\int_1^2\int_1^2 (x+y+z)^4 \, dx\, dy \, dz$$
as follows:
...
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Numerical integration of iterated integral with piecewise integrand
I need to plot the following integral:
$$
\Omega(t)=\int^{x_1(t)}_0 {4\pi x_i^2\rho(x_i,t=t_s)\int^\infty_04\pi x^2\rho_{reg}(x_i,x,t)dx}dx_i
$$
where
$$
\rho(x_i,t)=
\left\{
\begin{...
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1
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Trouble evaluating an expression [closed]
I am currently trying to numerically evaluate an expression which is the following. The expression IntD0 is being plotted, but the next line is not. I thought it ...
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130
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Wrong derivative in delay differential equation initial data returned by NDSolve
I have an DDE:
sol = NDSolve[{x'[t] + x[t - 1] == 0, x[t /; t <= 0] == t^2}, x, {t, -1, 5}]
And result (take the curve on the time interval $-1<t<0$)
<...
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3
answers
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Iterative pde solution NDSolve && NIntegrate
I try to solve a diffusion pde depending on a timedependent argument.
Step by step I have no problem to evaluate several solutions:
first step (timefunction 0):
...
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1
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2
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the Bessel function Integration
I try to calculate the integral of the Bessel function in Matlab
syms a r b k
L=int(log(r) * (besselj(0,a * r)+b * bessely(0,a * r)),k,1)
but I have this error (...
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1
answer
53
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How to improve the accuracy of integration with Bessel function without significant drop in performance?
Consider the following function and integral:
...
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How to make this kind of integration with the trigonometric function?
I am trying to make the following integration. But I am not sure about the result obtained as follows.
Is there some way to get more reliable and accurate results?
Thanks.
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Why are the results different when I integrate an expression in different ways?
When I integrate the expression like,
...
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Difference in the output of NIntegrate versus Integrate
I have an expression which when integrated, should be a cumulative distribution function (CDF). I have integrated the expression using both NIntegrate[] and Integrate[]. When the CDF returned by ...
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Solve PDE with consraints
I am trying to solve the following problem of the free fall dynamics under gravity of a inextensible horizontal string attached at its end, in a 2D vertical plane. If I'm right, that is the governing ...
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What is an appropriate setting in NDSolve to get feedback about the progress of a long computation?
Often in computation with an NDSolve-type solver, one hopes to know about its progress.
To this end, I am using StepMonitor as follows,
...
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Catastrophic loss of precision calculating Fox-H integral
I'm trying to numerically calculate the following Fox-H integral
$$
1-e^{-100}\sqrt{\frac{x}{\pi}} \left(\frac{1}{2\pi j}\right)^2\\ \oint_{\mathcal{L}_1}\oint_{\mathcal{L}_2} \frac{\Gamma(z_1)\Gamma(...
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Implementing the 3D Radon transform
I am wondering how to implement the Radon transform, the 3D Radon transform, that is, given a 'density' function $f: \mathbb{R}^3\to \mathbb{R}$ The Radon transform of $f$ is $$Rf(s,w)= \int_{x\cdot w=...
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Matrix Integro-differential equation
I'm trying to solve this integro-differential equation to obtain the density matrix elements $\rho$.
$
\frac{d\rho}{dt}=-i[H_{0}(t),\rho(t)]-A^{2}\Big[H_{1},\int_{t1}^{t}e^{-B(t-s)}\Big(e^{-i\int_{s}^{...
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Problem with a DAE and DiscreteVariables (II)
I continue with a DAE problem similar to another one posted here some days ago. @bbgodfrey offered a solution for the DiscreteVariables problem but now I have a ...
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2
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Solution on nonlinear pde with intial condtion
It produces an error. please suggest an alternative solution to the above-coupled pde problem.
...
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1
answer
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Solving system of equations including numerical integrals over region
I am dealing with the resolution of a concrete beam. Simply put, it is an equilibrium of horizontal forces and moments.
Let's first define some parameters :
...
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answer
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How to solve the error information in numerical integration and solve Sp?
How to solve the error information in numerical integration and solve Sp?
The codes are as follows:
...
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3
answers
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Infinite Integral involving a Bessel function
I have trouble evaluating the following numerical integral,
$$
\int_{0}^{\infty} d k^{(yz)} \, k^{(yz)} J_{0} \left(d^{(yz)} k^{(yz)} \right) \frac{e^{-i d_x \sqrt{k_R^2 + {k^{(yz)}}^{2} }}}{ \sqrt{...
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Why this integral gives zero?
I would like to compute this integral for a =100, ... ,1500
$$ \int_1^\infty \dfrac{\left(x^2-1\right)^{3/2}}{x} \,e^{-ax}\, dx $$
...
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Solving this system of differential equation with NDSolve
I'm trying to solve this system of differential equation (the ones in yellow markers are just constants):
The initial conditions for this system are n(0) = NN, na(0) = Na, n'(0) = q(0) = 0, q'(0) = ...
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Analytical integral running slow
I am calculating an integral with Mathematica, but it is running super slow!
Do you think there is a way to speed up the computation of A3? Maybe I should define my functions in a different way, but I ...
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Need help solving iterativelly a set of transcendental equations with NIntegrate
I have two sets of equations:
$q = \frac{1}{\sqrt{2 \pi}}\int dz~ e^{-z^2/2}F(q,\phi;z,\beta,\Delta, J) $
$\phi = \frac{1}{\sqrt{2 \pi}}\int dz~ e^{-z^2/2}G(q,\phi;z,\beta, \Delta, J) $
As you may see ...
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answer
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Why does NDSolve[] want to treat my equations as Delay Differential Equations?
I use NDSolve command (method->equation simplification -> residual) to solve different sets of Ordinary differential equations (ODEs).
It had worked alright till I added rather a simple ...
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Problem with a DAE and DiscreteVariables
Cross-posted in Wolfram Community.
I am solving an DAE problem with NDSolve. It is a physical problem related to friction forces: one mass on the X axis and ...
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NIntegrate fails to converge to desired accuracy
I am calculating an integral with Mathematica. This is the code I am using:
...
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How to make an integral and reproduce its graph
How by Mathematica we can make the integral, equation (101) in
arxiv:1307.5949
$
H_0(t-t_0) = \int^{\frac{a}{a_0}}_1 ~ \frac{da’}{\sqrt{ \frac{\Omega_r}{a’^2} + \frac{\Omega_m}{a’} + \Omega_\Lambda ...
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Compute area enclosed in a curve on a surface
Let's consider a 2D smooth surface embedded in 3D shown in the figure below. The corresponding metric tensor in Cartesian coordinates is
\begin{equation}
h = \biggr(\matrix{1 + \frac{A^2\pi^2}{4} \sin^...
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