# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### Getting an error with NIntegrate due to insufficient WorkingPrecision or divergent integral

Hello I have the following problem. But when I try to solve it, I get an error saying 'Catastrophic loss of precision in the global error estimate due to \ insufficient WorkingPrecision or divergent ...
59 views

### NDSolve problem in Mathematica 10.1, possible bug

The following code, ...
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### NDSolve for a system of nonlinear coupled pde

I try to solve a system($n$) of coupled nonlinear 1-d PDE's which is basically coupled sine-Gordon equations (through 2nd spatial derivative) in time and space. I am interested in the dynamics when I ...
415 views

### How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
112 views

### 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 ...
31 views

### Optimizing NMinimization and NIntegration with a Nested List-Valued Function

I want to use NMinimize and NIntegrate on each element of a nested list-valued function. Here's a simple example of what I'm ...
79 views

### Numerical integration plot

I am trying to do a numerical integration plot in Mathematica. Specifically, I want to plot $r$ versus $\tau$ where, $$\frac{dr}{d\tau}=\sqrt{2F(r)}$$ $F$ being a quartic polynomial. The limit of $r$ ...
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### difficulty in numerical estimate of double integral

I entered the following simple integral in mathematica: ...
1k views

### Using a compiled function inside NIntegrate gives “CompiledFunction::cfsa” message

The following function is defined for Real input: ...
260 views

### 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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### Why does Mathematica 10.3.1 fail me on : Integrate[(x^3) [Log[2 Sin[x]]]^8, {x, 0, Pi}] [closed]

All it gives me is a pretty restatement of my original request. When I use WolframAlpha PRO, I get a result of 624510 and a visual representation of the area in question. I know the ends of the ...
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### Nested Numerical Integration [duplicate]

So I am trying to evalute the following Integral Numerically: $$\int_{\mathcal{J}^+(x_0)\cap\mathcal{J}^-(x_f)}^{}A(x_0,x_1)\int_{\mathcal{J}^+(x_1)\cap\mathcal{J}^-(x_f)}^{}A(x_1,x_2) dx_1dx_2$$ ...
195 views

### 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 ...
101 views

### How to find the integrand singularity points when having NIntegrate::slwcon:

In order to calculate the closed area of the curve below defined by parametric equation curve02, ...
51 views

### My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
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### ND on a function using NIntegrate

I need to numerically differentiate a function that takes a list as an argument and that uses NIntegrate in its definition. A simple example is ...
44 views

### Numerical Integral with Boolean as part of argument

I am trying to numerically calculate a partial surface area integral of an oblate spheroid in spherical coordinates. The area I want to calculate is determined by a boolean function in the argument of ...
569 views

### Applying l'Hôpital's Rule to NDSolve with Piecewise Function

OK, so I've been working on this problem for over a week and it's driving me crazy. I'm trying to solve a system of two differential equations in $x(t)$ and $y(t)$ using a "time-elimination method," ...
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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 ...
56 views

### Singularity treatment in a simple problem [duplicate]

With a simple search, several posts can be found on treating singularities encountered while using NDSolvefamily of numerical methods. However, most of them involve ...
65 views

### Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
194 views

### Maximum of NDSolve output. Problem with interpolating function

I solve a NonLinear PDE and get a solution (which for other reasons I put into a vector): SolVec1[1][[2]][x,t], where x and t are the indipendent variables. Now, I would like to get a distribution ...
34 views

### Maximum of an integral that depends on a parameter [duplicate]

I have defined a function f(x,t) : ...
83 views

### 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 ...
78 views

### NFourierTransform do not show all points, even change PlotPoints and Exclusions

Needs["FourierSeries`"] I try solve the numerical Fourier transform of this function: ...
121 views

### Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
41 views

### 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 ...
96 views

### 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 ...
166 views

### How can I perform NIntegrate with NDSolve?

I'm a new user and I have no idea how to perform NIntegrate by using NDSolve. For example consider following differential equation (DE): ...
121 views

### 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}{\...
112 views

### 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 ...
81 views

### NIntegrate discrepancies

I want to compute a numerical integral for a gaussian trivariate distribution. Say ...
2k views

### Determining which rule NIntegrate selects automatically

I need to numerically integrate a highly oscillatory function over the semi-infinite domain $(0,\infty)$: $$\int_0^\infty \frac{\sin^2(x) \sin^2(1000 x)}{x^{5/2}}\mathrm dx$$ Since the Levin rule (...
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### Where did I go wrong with my implementation of the trapezoidal rule?

One method for doing quadrature, called the trapezoidal rule, improves accuracy by connecting the points on the curve corresponding to the points of subdivision with line segments, forming trapezoidal ...
907 views

### Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
383 views

### What do these error messages mean when numerically solving differential equations?

I am using Mathematica to numercially solve the following equations: ...
103 views

### 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 ...
110 views

### 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 ...