# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### How can I automatically set an NIntegrate call to zero if NIntegrate::slwcon is observed?

This is a generic question about the NIntegrate function. I am attempting to numerically integrate a function which may or may not be highly oscillatory, based on it's inputs. For a certain sets of ...
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### Discontinuous boundary condition in NDSolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $\cases{ U[0,y,t]=0,& if$0&...
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### Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
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### Maximum of an integral that depends on a parameter [duplicate]

I have defined a function f(x,t) : ...
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### Force WhenEvent to respect default stepsize

I have to numerically integrate an equation system and monitor the accumulating datapoints. For example, I fit a line to a subsample of the points and terminate via ...
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### What's the proper way to 'cut out' an irrelevant part of an integral, so I don't run into problems with precision?

I'm doing a numerical integration that involves an integrand with a few exponentials whose values over the integration region range enormously. I'm really only interested in the part of the range that ...
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### Problems with NDSolve for solving coupled Schrödinger-like PDEs with perfectly matched layer boundary condition

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
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### Difficulty using NDSolve

I am tying to solve two differential equations with two delays numerically. The result didn't come out and it was written that “NDSolve::ndsz:...step size is effectively zero; singularity or stiff ...
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### NFourierTransform do not show all points, even change PlotPoints and Exclusions

Needs["FourierSeries`"] I try solve the numerical Fourier transform of this function: ...
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### NIntegrate a function in a circular segment

I am trying to integrate numerically a function over a circular segment surface using polar coordinates. In the following example I am using the zero order Bessel function, but any cylindrical ...
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### Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
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### WorkingPrecision and AccuracyGoal for using with NIntegrate

I'm modeling a quantum tunneling barrier. Because I want to express my quantities in mks units, that means that some of the variables I'm using are pretty small (10^-9). I use NIntegrate for part of ...
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### Numerical approximation using trapezoidal formula [closed]

I have bumped into a problem, that I cannot solve. I have to approximate the value of ln3 using a composite trapezoidal formula, so that the error should be within (10)^-3! How can it be solved?
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### Trying to find a temperature profile with a nonlinear 2nd order ODE. NDSolve very sensitive to seemingly arbitrary constant

I am trying to solve this differential equation for a heat transfer problem: kt\frac{\partial^2 T}{\partial x^2} = \epsilon \sigma T^4, \ \ \ T(0) = T_0, \ \ \ \frac{\partial T}{\...
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### NIntegrate crashes without error message when using high precision integrand with non-zero tailing digits

I have a numerical integral that evaluates fine for floating point arguments with low precision (e.g., 4 digits), with argument where only zeros follow the first, e.g., 4 non-zero digits, or with ...
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### How do I extract the weights used by NIntegrate?

I'd like to use NIntegrate to adaptively integrate an expression, then use the same points and weights to integrate that expression with some parameters changed. I ...
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### Implementing the Numerov method for solving ODEs with NDSolve

I'd like to implement the Numerov scheme for solving an ODE (Scroedinger Eq time-independent) with NDSolve. I tried in analogy with the Runge Kutta example in the ...
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### NIntegrate discrepancies

I want to compute a numerical integral for a gaussian trivariate distribution. Say ...
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### Convergence data for Monte Carlo NIntegrate

I am using NIntegrate with Method -> "MonteCarlo" to evaluate a high dimensional integral. Is there a way I can obtain a list ...
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### Is it possible to get the exact value of the integration?

I have the following code in Mathematica. ...
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### Export NDSolve data

I have calculated a solution of a system of differential equations using NDSolve and generated a plot. How could I extract the data of the solutions? The input is ...
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### How to solve equation which has three variables and integration?

My equation is in the form x^2+y^2+50[Integrate[Exp[-P^2/10]*Log[(x + y*p + 1)/(x - y*p - 1)],{p,0,100} The range of x and <...
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### NIntegration and DSolve with same variable

I need to solve this problem: Then follows the code, with: ...
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### Plotting the image of a curve under a flow

I have some explicit time-independent vector field on the plane, and I would like to study how points evolve under the flow generated by this vector field. The flow is rather complicated and cannot be ...
284 views

### Using NIntegrate to integrate functions with sharp peaks (Lorentzian-like)

I have a problem with NIntegrate that I do not understand. I want to integrate a function f[x], which has a complicated analytic ...
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### Why is NDSolve's StartingStepSize with ExplicitEuler not working? How do I set the step size?

Why do I get a smooth curve (that is obviously wrong) when I run this? ...
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### DerivativeFilter[] is scaling down the data by ~100 or so, not a true differentiation? [duplicate]

I'm running the following function vzz = DerivativeFilter[z["Path"][[All, 2]], {1}]; But if I then integrate vzz the output z is about 100 smaller than the ...
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### How to couple NIntegrate with FindMinValue

I have a problem with a correct transfer of values of parameters when NIntegrate (and some subsequent functions) are coupled with minimizing procedures in ...
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### Reaction-diffusion PDE with NDSolve: either very slow or very inaccurate

I am struggling to have Mathematica 10.3 solve a system of PDE's (with periodic boundary conditions and random initial conditions), but either it produces a set of very noisy InterpolatingFunction ...
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### Multiple stopping constraints in NDSolve

I need to numerically solve several differential equations, with several constraints, like this : ...
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### numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
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### How to Minimize an NIntegral

My problem is to minimize in Mathematica a numerical integral. The command FindMinimum[With[{R=2.5},NIntegrate[(R*r1*a)*Sin[r1*a],{r1,1,R}]],a] does calculate ...
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### How to define an exclusion zone for NDSolve

I need to numerically integrate a differential equation and define two exclusion zones to stop the integration. The Mathematica code looks like this : ...
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### Split Boundary Value Problems win Algebraic Equations

Is it possible at all to solve with NDSolve (or other built in function) a split boundary value problem with algebraic equations? Please look at the following example: ...
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### Integration by using NDSolve [duplicate]

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
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### How to integrate a Bézier function?

I have: points = {{0, 100}, {250, 0}, {0, 300}, {500, 500}} And I want to know the area below the curve, so I came to: ...
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### FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
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### Multiple numerical integrations and green's functions propagation of the solution

I have to solve a system of equations where the coefficients have to be computed from numerical integrations. My problem is that my codes is to extremely slow because I each time that it has to ...
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### NIntegrate (Helium Singlet and Triplet) [closed]

I have two integrals that I am calculating using nested NIntegrate. One is for the singlet helium atom and another for triplet. (here, I am calculating variationally the approximate energies and ...
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### Mathematica 10.2 is slow to NIntegrate highly oscillatory integrals

I noticed that Mathematica V10.2 is taking much longer to run my code when compared with V9. One function that seems affected is NIntegrate. For example, for a ...
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### How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
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### Integration with IntervalMemberQ

I define an interval and its associated index function. ...
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### Numerically integrate a plotted function

I used Plot[NIntegrate[...]...] to plot a function of 5 different variables. It took really long. Right now I need to integrate this function one more time over the ...