Questions tagged [numerical-integration]

Questions on the use of numerical functions NIntegrate and NDSolve.

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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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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)+\...
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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 ...
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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: ...
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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 ...
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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. ...
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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 ...
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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, $$\...
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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: ...
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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 <...
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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, ...
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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 ...
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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. ...
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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 ...
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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 ...
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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. ...
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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 ...
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1answer
238 views

2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
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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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 ...
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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 \...
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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)...
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2answers
95 views

Is there any faster alternative for matrix exponential?

Lets define matrix $M$ as ...
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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 ...
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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 ...
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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 ...
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1answer
126 views

How to combine NDSolve interpolating functions?

In the following working example ...
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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^{...
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1answer
40 views

Plot solution of ODE with singularity

I wish to plot the solution of the following ODE: ...
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 ...
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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: ...
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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
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2answers
115 views

Error test failure when solving two coupled ODEs

by NDSolve; this is work until y=6.22 ...
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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 <...
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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 ...
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0answers
15 views

Exporting output from many NDSolve's to common .txt [duplicate]

Let there be the following working example ...
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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 ...
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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 ...
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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}}}...
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1answer
35 views

Internal precision limit reached?

The following piece of code ...
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3answers
76 views

How to efficiently choose methods in NIntegrate

I recently compute it. ...
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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. ...
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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: ...
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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
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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
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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 ...
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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"] ...
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2answers
66 views

NIntegral failing to converge

I have the following integrals that I am trying to calculate: ...