Questions on the use of numerical functions NIntegrate and NDSolve.

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1answer
146 views

Slow evaluation of NIntegrate when used as a pure function

I asked a perhaps related question here. Here is my code in below. The goal is that to define a function which must be integrated numerically. The function itself first is calculated over different ...
3
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1answer
227 views

Numerical integration's speed

Consider this numerical integration of Bessel function: Do[NIntegrate[BesselJ[2, x], {x, 0, 10000}], {i, 1, 100}] // AbsoluteTiming {4.033403, Null} This is ...
6
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2answers
165 views

How to force Mathematica to throw an error for NIntegrate

Consider this: NIntegrate[BesselJ[2, x], {x, 0, Infinity}] 0.9999999999904574 This is the correct answer. Now: ...
6
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1answer
148 views

Strange Behaviour of NIntegrate

I found some of the values remained unevaluated using the following code Table[NIntegrate[Sin[i x]/((2^x + 1) (Sin[x])), {x, -Pi/2, Pi/2}], {i,70, 90}] Pick them ...
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2answers
236 views

Wolfram Alpha will calculate this definite integral but Mathematica won't

I'm trying to compute a definite integral of the form $$\int_{0.2}^{0.5} \frac{1}{(1 - y)y^2\sqrt{0.5 - y^2 + y^3}}$$ in Mathematica. WolframAlpha will calculate this but Mathematica only outputs the ...
1
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1answer
54 views

WhenEvent error in NDSolve

I’m trying to solve a discontinuous differential equation where there are lost of energy when the trajectory cross the discontinuous manifold. The code I used was ...
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0answers
36 views

NDSolveValue:dsvar error in a system of non linear differential equations generated using a Table

I have a system of 4 non-linear differential equation, that I generate using Table command. On solving, I keep getting a dsvar error that is not going away. I debugged my code and figured it has to do ...
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0answers
82 views

Extrapolation of area for a 2D integration

I have a set of points distributed almost uniformly in a certain area of a 2D plane as follow: An example of data points (orange) data = {{0.919443, 1.68921*10^-22}, {0.262277, ...
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2answers
88 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
1
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2answers
223 views

Real integral evaluates to imaginary number

The following integral:Integrate[Exp[-2/3 Log[1 + x^3]], {x, 0, 1}] is evaluating to an imaginary number. Its closed-form expression should be ...
1
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1answer
148 views

Line integrals over a path defined by a set of points (rather than an analytic formula)

I'm getting inaccurate results when computing (plotting) the value of a function against the length of a line integral, where the path comes from a set of numerically calculated points. (In contrast, ...
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0answers
60 views

How to properly pass function as argument here? --> NMinimize & NIntegrate involved

I had a problem of a similar kind here which was solved. Now after changing a few things in my problem setting I am suffering from the following problem. Let me first introduce methods/functions that ...
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0answers
37 views

NDSolve dependence on initial values

I'm checking some results in this paper and I'm currently having some issues with a numerical integration of a set of differential equations using NDSolve (section 2 and 3.1-3.2 in the paper). I'll ...
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0answers
66 views
0
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1answer
55 views

Numerical integration of a three dimensional array

I need to integrate a scalar valued function $f\left(\boldsymbol{x}\right)$ where $\boldsymbol{x}$ is a three dimensional position vector; in other words: $\int_{\Omega} f\left(\boldsymbol{x}\right) ...
1
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3answers
97 views

I know the lower limit of an integration as well as the integral. How to find the upper limit of the integration?

I used the following code. NV[x1_, x2_] := NIntegrate[3 x^2, {x, x1, x2}] FindRoot[NV[0, t] == 3, {t, .001}, PrecisionGoal -> 20] Output: ...
2
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2answers
154 views
2
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2answers
218 views

NIntegrate 2D highly oscillatory function

I am trying to integrate a function, and the error I get is greater than the result. So I need to calculate ...
1
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1answer
44 views

Problem with NIntegrate over a user-defined region

I define a region as follows: ...
3
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0answers
97 views

Obtaining NIntegrate error estimate

Is there a way to extract the error that Mathematica estimates when calculating a numerical integral using NIntegrate? Internally Mathematica must keep track of this error, because it is used to ...
0
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1answer
90 views

NIntegrate vs. summation

I' m interesting in distributions of points on sphere, plane figures etc. Especially for small number of points: 1, 3, 7, ... It seems that good criterion for uniformity of distribution is some ...
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0answers
28 views

Tricks to speeding up optimisation of a function involving a heavy integration

This is the code, and energycoeffs[] is the function that takes in a dxd matrix and spits out a scalar value. ...
0
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1answer
65 views

Integration does not give real value

The code below must be obvious. We are trying to integrate a complicated function from 0 to 1. ...
1
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2answers
153 views

Problem with FindMinimum

I am struggling with a problem on fitting a function to my data using FindMinimum. The problem is related to small angle x-ray scattering and my approach is the following: I define the electron ...
0
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1answer
41 views

Problems using a complicated function within a LogLinearPlot [duplicate]

my problem is that I have a rather large function which I'm trying to plot, which looks something like this: ...
2
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1answer
112 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
3
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1answer
110 views

What boundary is added when NDSolve::bcart pops up?

When insufficient boundary conditions are given to NDSolve for solving PDE, the warning NDSolve::bcart pops up: ...
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2answers
93 views

optimization of CountourPlot with NIntegrate

I have to use ContourPlot with a complicated function depending on 2 parametrs (that I cannot report here) that contains numerical integrations. Here is a simple ...
2
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3answers
144 views

Inefficient NIntegrate and Which

In version 10 a simple numerical integraton of piecewise function is highly inefficient: ...
2
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1answer
87 views

NIntegrate and Integrate giving different results for ill-behaved function

I'm trying to integrate the following function with Mathematica 8: $$ I(a,b)= \int_0^1 \mathrm{d}x\int_0^1\mathrm{d}y \,\theta(1-x-y) \frac{1}{x a^2-y(1-y)b^2},$$ where $\theta$ is the Heaviside ...
1
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1answer
92 views

Implicit region misses subset?

Context I am interested in integrating a 2D function over lines defined implicitely Attempt Let me just start by integrating the identify on such sets of lines which a defined using ...
5
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1answer
95 views

Integrate over implicit 1D region: works for algebraic but not transcendental equation?

QUESTION How come this works: NIntegrate[1, {x, y} ∈ ImplicitRegion[{x == y^3, x <= 1, x >= 0}, {x, y}]] But this fails: ...
6
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1answer
118 views

Numerical Integration different in Mathematica version 9 and 10 with same options

I have noted that the same function with the same settings gives me different results in Mathematica version 9 and 10. This involves integrating numerically interpolating functions and so on. Here a ...
1
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1answer
138 views

Solving a nasty partial differential equation

I have a differential equation that I would like to solve numerically in the region $z \in [0,L]$ and $t \in [0,t_{max}]$: $$ \partial_t S(z,t) = f(z)S(z,t) + \int_0^L \text{d} z'g(z,z') S(z',t), $$ ...
3
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1answer
197 views

What method does `NIntegrate` uses by default?

There is a variety of algorithm for performing numerical integration (See wiki). What method does NIntegrate uses by default? I looked on the documentation page and I saw that the function ...
0
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2answers
93 views

NIntegrate and Integrate of a Spherical Bessel function

I am trying to integrate over a spherical bessel function. I have used both the Integrate and NIntegrate functions in Mathematica but the values given by each do not match. Any reason why this ...
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1answer
95 views

How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
2
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1answer
84 views

How to obtain numerical answer for equation containing integration

Could some one tell me how to obtain numerical value of $a$ and $b$ from equations below: $$\frac{1+exp(b)}{1+exp(0.9a+b)}=0.95$$ $$\int_{0}^{\infty} \frac{1+exp(b)}{1+exp(a x+b)}=1$$
1
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1answer
65 views

Finding the true expectation

I have the density function and I want to determine its expected value ...
3
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0answers
137 views

Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...
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0answers
80 views

Numerical Integration/Function

I have a problem with a function defined numerically through an integral of the form: ...
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0answers
27 views

What means the definition F[t_?NumericQ] :=…? [duplicate]

I've come along a function defined in this way: F[t_?NumericQ] := NDSolve[{-u''[x] - u[x]/x == -t^2 u[x], u[x0] == x0, u'[x0] == 1}, u, {x, x0, x1}] What does ...
1
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1answer
157 views

Runge-Kutta Butcher tables

I like to have the Butcher's table for Explicit (or implicit as well) Runge-Kutta method of a fixed order. I do not understand reading ...
0
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1answer
65 views

NDSolve not able to solve a system of differential equations

Here are some basic equations ...
15
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2answers
246 views

Least effort to handle a point source inside the domain of PDE(s)

By point source I mean a constrained condition at one point inside the domain of PDE(s). For example: $$\frac{\partial ^2u(t,x,y)}{\partial t^2}=\frac{\partial ^2u(t,x,y)}{\partial ...
0
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3answers
91 views

Calculate this integral returns undefined

Limit[ (Integrate[Sqrt[Exp[3 t + 2] + 3] , {t, 0, x}]^2) / Integrate[Sqrt[Exp[6 t - 2] + 5] , {t, 0, x}] , x -> Infinity] This can be solved but ...
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0answers
62 views

Locating Periodic Orbits - Part II

In a previous post Part I I asked how could I locate the x0 position of a periodic orbit. I got only one possible solution but it does not work as I want. Let me be ...