# Questions tagged [numerical-integration]

Questions on the use of numerical functions NIntegrate and NDSolve.

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### How i can calculate the following integrals [closed]

I have the same interval but now a take anothe distribution Pareto. ...
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My code is: ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
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### 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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### 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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### Plot solution of ODE with singularity

I wish to plot the solution of the following ODE: ...
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### 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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### 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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### 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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### Error test failure when solving two coupled ODEs

by NDSolve; this is work until y=6.22 ...
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### 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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### 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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### Exporting output from many NDSolve's to common .txt [duplicate]

Let there be the following working example ...
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### 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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### 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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I'm trying to integrate an expression I have for a PDF $$p(L, \eta)=\int_{0}^{\infty} \mu \tanh (\mu \pi) P_{-1 / 2+i \mu}(\eta) \exp \left[-\left(\mu^{2}+\frac{1}{4}\right) \frac{L}{L_{\mathrm{loc}}}... 1answer 35 views ### Internal precision limit reached? The following piece of code ... 3answers 76 views ### How to efficiently choose methods in NIntegrate I recently compute it. ... 1answer 95 views ### Help in finding a good guesses for ode This problem solved in 1 by @bbgodfrey. However, when I changed the parameters, the ode becomes very stiff and I did not know which best guess I need to use for y0. ... 1answer 37 views ### Interpolation of a “bit by bit” Function I am facing a problem with integrating a function. I have to integrate the function "bit by bit". This is the smallest working example that shows the problem: ... 0answers 47 views ### What is the best method for numerical integration of this one I have an integral as follows$$\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 ...
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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/...
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### 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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### 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"] ...