Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
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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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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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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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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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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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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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NIntegrate issue without any singularity
I'm evaluating an integral using NIntegrate, I checked the expression and there shouldn't be any singularity at least on paper. The parameter ...
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Integration does not converge in iteration
I have the following code to find a numerical solution for a singular BVPas attached in the picture. I have the following Mathematica code: (This code of this question can be found at Mathematica does ...
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PDE with tangential derivative condition along boundary. NDSolve not working
I'm considering the following PDE
$$
\begin{align}
\left[\cos\theta\frac{\partial}{\partial r}-\frac{\sin\theta}{r}\frac{\partial}{\partial\theta}\right]\left[\sin\theta\frac{\partial}{\partial r}+\...
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How to remove error in NIntegrate
I want to solev NIntegrate in two dimension. But when i run the code i got Throw::nocatch: Uncaught Throw[-HolonomicDifferentialRootReduceDumpy[NIntegrateLevinRuleDumpx]+(...
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I want to solve Integrate [duplicate]
I am wondering why I am receiving the message "The integrand ... has evaluated to non-numerical values for all sampling points in the region ..." for a particular calculation I am running. ...
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Avoid imaginary result FindRoot
I have a code where I'm using FindRoot for the equation toroottp. I plug in some sample values on ...
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Looking for an appropriate method of NDSolve for dynamical system
I am dealing with the numerical solutions of a variety of dynamical systems with integrals of motion.
As the example, let me consider the Kuramoto model, which equations of motion are
...
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Integration over an implicit region
A question asks me to calculate the following integral using NIntegrate:
Calculate the double integral ... where D is the area bounded by the four lines ...
With ...
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Getting a wrong plot after NIntegration
I am trying to plot this function numerically.
R2T = ...
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1
answer
117
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Speeding up Boussinesq equations solving?
I am working on Boussinesq equation. The notebook can run perfectly for only 0.6 steps and then the calculation starts running slowly after 0.7. All boundary conditions seemed fine. I am unsure if I ...
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Problem with NIntegrate a solution of NDSolve
I'm having trouble making a function that uses the result of NDSolve:
...
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Can Mathematica calculate this elliptic, triple integral?
Integrate[(4 a b/Pi) (a^2 + b^2 - 2 a b Cos[c])^(1/2), {a, 0, 1}, {b,
0, 1}, {c, 0, Pi}]
I'm using basic plan, it gives me the result like that.
The ...
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BVP with 2nd order coupled ODEs
I get the following error messages:
Infinite expression 1/0. encountered.
Indeterminate expression 0.\ ComplexInfinity encountered.
Encountered non-numerical value for a derivative at s == 0.1
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Why does Mathematica not know some integrals diverge?
I want to analyse the convergence of some complicated 1d integrals that may have divergences at $x=0$, similarly to the harmonic integral $\int_0^a 1/x \ \mathbb{d} x$, which I know is divergent.
When ...
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NDSolve: there are more variables than equations, underdet
I am working on using NDSolve to solve coupled ODE. The following is the coupled equations. It works fine for sever orders. I used table to generate like 962 couple variables and equations, where the ...
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Numerical solution of an advance-delay ODE with multiple advances and delays
I am trying to solve a differential equation of the form
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I am unable to plot 3D graph of integral function
I am not able to solve this integral
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How to make the NIntegate of two variables as efficient as possible
I asked my question here (Multivariable NIntegrate gives different value if I integrate it separately), I think the best way to get help is by putting the original code here. So, my question is how ...
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NDSolve overdetermined but I can't see how
Edit: partial answer
This confuses me but it is due to some behaviour of pattern matching which just seems wrong to me.
An example of the behaviour
...
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Multivariable NIntegrate gives different value if I integrate it separately
I have a double variable integral, so I can define a function which is the integration of the other variable, and finally, I integrate the other variable. here is the code:
...
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Too big error of numerical integrate
I want to do some numerical integrate with Mathematica, but the results are very different from others' result calculated by C code. Here is my code:
...
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Inconsistent results between NIntegrate and Integrate
I get these inconsistent results
What is going wrong? Fast oscillating terms? Small exponential factors?
But then, why the result seems to toggle between values 1 and 2, rather than being a real ...
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Solution of NDSolve evaluates pointwise, but won't plot (possibly due to issue with FindRoot and replacement rules)
I'm trying to solve a pair of uncoupled differential equations using NDSolve, where the initial conditions are determined by FindRoot. Here's the relevant section of the code, including error message. ...
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Integration of accelerometer data to x-y-z position [closed]
Hi I have a list of accelerometer data, in their xyz acceleration values.
May I ask how can I integrate these data to get to the position in their xyz angle, assuming the initial velocity is zero and ...
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NIntegrate can't integrate function but work fine with the expression [closed]
I have a function called psi0 that looks like this: psi0 := E^(-(x - 10)^2/10) and I'm trying to integrate it numerically from 0 to a variable L. However, I keep ...
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Problem with NIntegrate and more general problems with NDSolve
I'm new to Mathematica and I'm receiving little help for a (to me) quite difficult problem I'm trying to solve. I want to solve logarithmic Boltzmann equation for abundance of dark matter.
I'm having ...
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Choosing spatial direction in Method of Lines
Edit:The temporal variable can be set using
Method -> {"PDEDiscretization" -> {"MethodOfLines","TemporalVariable" -> t}}
...
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Poincare section for a perturbed string
I am trying to find the Poincare section of a perturbed string in a gravitational background with a magnetic field. The plots that I am trying to reproduce are from this paper (page 11).
The code that ...
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Non Linear System of Diferential Equations with periodic function
I am programming a system of differential equations consisting of 3 cell populations; Normal cells N, Tumor cells T and chemotherapy treatment Q, when a function q is constant. The system is as ...
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Numerical integration of highly oscillating function
I want to Numerically integrate the following function
...
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How to do double numerical integration one of the variables integrate to another one
Here I have an express with two variables like ...
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Simple 3D trapzoidal rule gone wrong
I am trying to implement a 3D trapezoidal rule function, but I get wrong result and I do not understand what's wrong. Here is the code:
...
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