Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
2,288
questions
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28 views
How i can calculate the following integrals [closed]
I have the same interval but now a take anothe distribution Pareto.
...
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2answers
65 views
0
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1answer
34 views
Shooting with updating BC's
So I have a 'fairly simple' problem that needs to be 'solved'. I have been able to solve this running 2 loops in Matlab but I am sure Mathematica should be able to handle this. I have the ODE $$F'(x)+\...
-2
votes
0answers
42 views
Complex Plotting In Matlab [closed]
I have got a function after integration in Matlab, $f(\theta,g)$ which is a complex function. I would like to get 3D plot the this function with respect to $\theta$ and $g$, where $g$ positive integer ...
0
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0answers
24 views
NDSolve error when integrating two second order coupled ODEs
I want to plot a solution for a system of two second order coupled ODEs:
...
1
vote
1answer
44 views
Adjusting PrecisionGoal and AccuracyGoal when solving my equation using NDSolve?
Thanks for paying attention to my question and modifying my terrible formatting[facepalm], now I think I've found the answer. The point is the selection ...
1
vote
0answers
66 views
How can I get this integral to Compute
I'm trying to compute the following expression and get an analytical answer but Mathematica ends up spitting back the input expression. Hoping someone can shine some light on this.
...
0
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0answers
69 views
Integration in matlab/ Mathematica [closed]
I would like to calculate the integration numerically and make a plot with respect to $\theta$. The integration is
$I=\int_0^T \langle\psi(t)\mid\frac{d}{dt}\mid\psi(t)\rangle$
where T is the time ...
5
votes
1answer
72 views
Nonlinear differential equation with unknown parameter and integral form boundary condition
I'm trying to solve numerically a non-linear problem in order to determine the velocity field ($U$) and the film thickness ($h$) of a non-Newtonian fluid over an inclined plane. The equations are,
$$\...
1
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0answers
90 views
How to calculate volume under f(x,y)
I have the following function:
σ = 0.3;
μ = 5;
cy =0;
cx=0;
f[x_,y_]=Exp[-(1/2)((Sqrt[(x-cx)^2+(y-cy)^2]-μ)/σ)^2]/(σ*Sqrt[2*π])
Plotting this with:
...
1
vote
0answers
33 views
Unexpected stiff system error [closed]
Let there be the following functions
ya[t_, x_] := Cosh[t*x]
za[t_, x_] := Sinh[t*x]
wa[t_, x_] := x*Sinh[t*x]^2
One can verify that the following PDE's hold
<...
1
vote
0answers
43 views
Numerical Artifacts in Schwarz-Christoffel (I think?) How to remove?
I have a problem that involves integrating a complicated Schwarz-Christoffel integrand. In order to test out my results so far, I've tried to give simpler integrands of the same type to Mathematica, ...
0
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0answers
66 views
A system of linear differential equations with variable (time-dependent) coefficients
I have searched almost all similar pages discussing a system of differential equations, but none of them discussed the case of variable coefficients. My problem is a bit more complicated, because ...
0
votes
2answers
36 views
Getting message NIntegrate::nlim when trying to integrate within a For-loop [closed]
I want to evaluate an integral that has integration limits x and 1.
...
0
votes
0answers
26 views
Inconsistency in complex line integral using 2 parameters vs 1 parameter
I am trying to numerically verify that, over a closed circular path,
the line integral of a physics-inspired complex quantity $z_Q = P \cdot \frac{\partial}{\partial Q} S$ is
the same regardless of ...
3
votes
1answer
94 views
Solving Piecewise Differential Equation using NDSolve (coupling at BC)
I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
4
votes
1answer
55 views
Calculating the volume of a paraboloidal region
I have an inequality that defines a paraboloid. I would like to calculate the volume of the intersection of this paraboloid and a cylinder of radius R.
...
2
votes
0answers
79 views
How to do fast numerical integration, while using Cuba Library package: Vegas [closed]
I want to do the numerical integration with singularities. Although NIntegrate does the job, But it takes too much time, so i want to use the Cuba library that offers a choice of four independent ...
3
votes
1answer
238 views
5
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1answer
133 views
NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two
I was in the impression that V12 can now handle higher order PDES but for this particular case it fails to produce any solution.
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0
votes
1answer
63 views
Plot a family of solutions of ODE with singularity
In the post Use Mathematica to plot the flow of an ODE with discontinuity, the following ODE with discontinuous coefficient was solved
...
2
votes
0answers
91 views
Model 1D Vlasov Equation
Vlasov Equation
The non-relativistic form of the Vlasov equation is given by:
$$
\partial_{t} f\left( \mathbf{x}, \mathbf{v}, t \right) + \mathbf{v} \cdot \nabla f\left( \mathbf{x}, \mathbf{v}, t \...
1
vote
0answers
63 views
How much can we trust NIntegrate when NIntegrate::eincr is shown? [closed]
I have been dealing with a high oscillation integration using NIntegrate. The warning of eincr shows that no matter how large (X)...
2
votes
2answers
95 views
1
vote
0answers
35 views
Two point Gaussian quadrature [closed]
I am trying to calculate a two point Gaussian Quadrature on the interval [0,4] and the function f_n = (x^n) + 2 x - 3 for ...
4
votes
1answer
104 views
Speed-up calculation of Area of Polygons
I have a complicated polygon in the 2d plane, that is an RegionIntersection of RegionUnion of triangles.
Finally, I want to ...
0
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0answers
94 views
Using NDSolve for differential equations
I'm trying to numerically solve the following differential equations eqs for plotting the bifurcation diagram. However, under special values of the parameter u, I get a problem when calculating the ...
7
votes
1answer
126 views
3
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1answer
80 views
Automatically Switch between Integrate and NIntegrate
I have an algorithm for which I need to compute some multidimensional
integrals. Sometimes, Integrate works but some others Integrate just fails
to compute the integral.
A simple example:
$$ \int^{...
2
votes
1answer
40 views
6
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1answer
74 views
How to help NDSolveValue handle the addition of another dependent variable in a set of reaction-diffusion equations
I am trying to use NDSolveValue to solve a system of coupled reaction-diffusion equations in a 2D space (technically 3D cylindrical coordinates, but due to radial ...
4
votes
1answer
63 views
How to calculate an area of a conformal map enclosed shape?
I need to calculate the area of a conformal mapping closed shape on the complex plane that gives the perimeter.
I have the following parameters:
...
1
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0answers
25 views
Weird result comparing the errorformula with the actual error using the trapezoid method [closed]
The graph I got using the code in the link is VERY peculiar to say the least. I have no idea what's causing it.
https://community.wolfram.com/groups/-/m/t/1840718?p_p_auth=PKMDl2TX
2
votes
2answers
115 views
0
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1answer
61 views
How to get the analytical solution or numerical solution of the double integral
i just want to calculate this double integral but can't get the analytical solution,so it there a way to get the analytical solution or numerical solution of the double integral?
codes are as this
<...
0
votes
1answer
32 views
Numerical Double Integral with symbolic bounds to normalize function
I'm trying to use mathematica to normalize this trial wave function which requires finding the following integral and solving for A so that the total propability equals 1. 'a' is the constant width of ...
1
vote
0answers
15 views
Exporting output from many NDSolve's to common .txt [duplicate]
Let there be the following working example
...
1
vote
0answers
30 views
NDSolve::underdet with long list of variables
I am trying to solve a huge system of DAEs. When I start the solution, NDSolve says NDSolve::underdet "There are more dependent variables...". I know about why this error occurs. I have lots of ...
8
votes
2answers
102 views
How can I reduce the number of function calls in my code?
Consider the code shown below. I was expecting e1[x1_, x2_, x3_] to be called same number of times as g1[x1_, x2_, x3_], but it ...
0
votes
2answers
64 views
Error while using NIntegrate [closed]
I'm trying to integrate an expression I have for a PDF
$$p(L, \eta)=\int_{0}^{\infty} \mu \tanh (\mu \pi) P_{-1 / 2+i \mu}(\eta) \exp \left[-\left(\mu^{2}+\frac{1}{4}\right) \frac{L}{L_{\mathrm{loc}}}...
1
vote
1answer
35 views
3
votes
3answers
76 views
2
votes
1answer
95 views
Help in finding a good guesses for ode
This problem solved in 1 by @bbgodfrey. However, when I changed the parameters, the ode becomes very stiff and I did not know which best guess I need to use for y0. ...
1
vote
1answer
37 views
Interpolation of a “bit by bit” Function
I am facing a problem with integrating a function. I have to integrate the function "bit by bit". This is the smallest working example that shows the problem:
...
0
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0answers
47 views
What is the best method for numerical integration of this one
I have an integral as follows $$\int_0^\infty r^k \psi(r) dr \tag{1}$$ where $$\psi=e^{-ar-br^2-cr^3-dr^4}\tag{2}$$ I tried NIntegrate It woks for some values but ...
2
votes
0answers
59 views
NDSolve Error “message text not found” [closed]
I am trying to solve a nonlinear PDE - 1D diffusive heat equation.
I'm not sure what is wrong (am new to Mathematica).
I'm trying to use https://reference.wolfram.com/language/FEMDocumentation/...
5
votes
1answer
142 views
Area of an Annulus (MeshTools<>NIntegrate)
In a very simple example I try to describe an annulus using MeshTools package
mesh2D = AnnulusMesh[{0, 0}, { 1 , 2 }, {-Pi, Pi}, {36, 10}];
The area given ...
1
vote
1answer
48 views
How to Double integrate a function Separately?
I have function f[x,y] where i need to integrate f[x,y] with x first and then later i need to integrate that f[x,y]dx with y.
I will be getting f[x,y]dx from another notebook after using Get["ffile"] ...
-2
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2answers
66 views
0
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1answer
86 views
