Questions on the use of numerical functions NIntegrate and NDSolve.

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1
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2answers
96 views

Problem evaluating a complicated integral

Apologies for stating my problem poorly in the first instance, thank you for the help in narrowing down the issue. Problem For those interested, it's for the exact unbiased inverse of the ...
2
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0answers
100 views

How to specify the time variable for NDSolve

I recall that it is possible to specify which independent variable is the "time" variable in NDSolve, but I can't find it documented anywhere. Does anyone recall ...
1
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0answers
91 views

Speeding up the numerical integration of a certain function

I'm using the following function f[t_] := 3/4 t^-3 NIntegrate[(x^4*Csch[x/2]^2), {x, 0, t}, Method -> {Automatic, "SymbolicProcessing" -> 0}]; I ...
0
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1answer
71 views

How to get correct numerical integration which should be zero? [duplicate]

I want to numerically integrate function berrycur over kx and ky. The definition of berrycur is given at the end of the ...
0
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1answer
477 views

wolfram mathematica intersection of two surfaces [duplicate]

I use wolfram mathematica. There is a function of two variables which defines the surface z = f(x,y), the second surface is defined as z = const. How to find the line of intersection of these two ...
0
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0answers
40 views

NIntegrate Issue: Changing integration limits makes calculation time extremely long

After a long time developing some code in mathematica and finally getting it to work, I have unfortunately encountered an odd problem: When I change the limits of integration (and shift the function ...
-1
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2answers
81 views

Strange numerical integration result

I write a function called berrycur[kx,ky] which I will give at the end of the question, and want to numerically integrate this function over {kx, -2π, 2π]}, {ky, 0, ...
0
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0answers
40 views

Comparing NIntegrate with definite integration

I want to calculate without error a sum of double integrals with the following definitions for the functions within them: ...
0
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1answer
70 views

Numerical integration with purely numerical integrand

I'm trying to perform a numerical integral with an integrand that should not be manipulated with any symbolic preprocessing whatsoever. Consider the following simple test : ...
0
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0answers
337 views

NIntegrate: integrand has evaluated to non numerical values

I have pasted a code that has been giving me some trouble and errors when I try to compute. ERROR: "The integrand 1435.1232 E^(-6.4703566*10^6 s^2) deEntrance[s,phi]^2 has evaluated to ...
1
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0answers
136 views

NIntegrate (multi-dimensional integral)

I am interested in the numerical evaluation of the following integral: $\int \prod_{i=1}^n dx_i \delta(\sum_{i=1}^n x_i) \prod_{i=1}^n f_i(x_i)$ where $f(x)$ is a complicated function. Unfortunately ...
3
votes
2answers
218 views

Integration and Fourier transform

I would like to calculate the distribution function from the characteristic function. There is a formula given as $$F_X(x)=\frac{1}{2}+\frac{1}{2\pi}\int_{0}^\infty \frac{e^{i w x}\phi(-w)-e^{-i w ...
5
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2answers
431 views

Calculating the area under a curve, but above a certain threshold value

so here I am with a time series of data (hours (t) and corresponding measurements (a)). ...
0
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1answer
126 views

NIntegrate: Catastrophic loss of precision

Below is a simplified code that I am trying to evaluate. I am basically getting the rms value of a Wakefield function. When I finally try to evaluate the rms, I get an error. Any help would be greatly ...
3
votes
2answers
116 views

NIntegrate returns zero for non zero integrand, 4d Integration

I am trying to calculate the following integral. ...
0
votes
1answer
69 views

Integrating function can't be epressed? [closed]

Hi I have a function in a form of $$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$ The code is Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}] But it can't work ...
6
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3answers
405 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m ...
1
vote
0answers
90 views

Code for solving numerically an integro-differential equation

First of all, I want to greet the community. This is my first question, but I hope I will be able to help answering others members questions, although I am quite new working with Mathematica. I would ...
0
votes
1answer
41 views

Calculate Integral with cos [closed]

Integrate[ (Pi/4 - x/2) cos (n *x), {x, 0, Pi}] This doesnt give me desired results .n is natural 1,2,3,4,5... I want to get something like ...
1
vote
1answer
125 views

NIntegrate failed to converge?

Hey guys I have a pretty simple code that consists of an RMS calculation. The issue is that I am getting quite a few error messages when I run it. The following equations are highly published physics ...
1
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0answers
68 views

Speeding Up NIntegrate and ?NumericQ

I have attached below a piece of code that has been running successfully but takes extremely long for mathematica to compute. I believe it is the last "rms" calculation and the fact that I am using ...
0
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1answer
46 views

Error message from NDSolve using WhenEvent

I am working with the following NDSolve expression: ...
2
votes
4answers
397 views

How to calculate this integral?

I am trying to Integrate the following Integral : $\int_1^{\infty } \dfrac{\left(x^2-1\right)^{13/2} e^{-ax} }{x^{10}} \, dx \,\, \,\,\,\,\,\,\,\,\,\,\,\,(a=\textrm{real>0})$ Mathematica didn't ...
2
votes
2answers
334 views

How to compute this triple integral? [closed]

In Mathematica how can I compute this integral:$$ \iiint_{D}\sqrt{(1-9z^2)(1-4y^2-9z^2)}\,dx\,dy\,dz$$ where D is the domain: $$D: x^2 +4y^2+9z^2\le1$$ Please I need help!!!
1
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1answer
565 views

Runge-Kutta 2nd Order ODE Solver

Suppose I have a 2nd order ODE of the form y''(t) = 1/y with y(0) = 0 and y'(0) = 10, and ...
1
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0answers
55 views

Multidimensional Numerical Integral with Singular Behavior [closed]

I'm trying to numerically integrate a multidimensional integral where there is singular behavior when x = y. This is the integral ...
3
votes
1answer
241 views

Integrating a functional of an InterpolatingFunction

It is straightforward to Integrate an InterpolatingFunction. However, even for a simple functional of an ...
7
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1answer
81 views

Unify the sampling of NIntegrate[ {f, g, h} w ]

I'm trying to numerically integrate a function which has a vector-valued slow part and a much faster component which is shared by all the components, i.e. an integral of the form $$ ...
0
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1answer
115 views

Better way to check conservation in NDSolve

The partial differential equation in the NDSolve below is conservative (by construction) of $\int_{-1}^{+1} p(t,z)\ dz$ for all $t$. ...
0
votes
1answer
156 views

Zooming into Parametric Animation Plot that Uses InterpolatingFunctions

I have an interplanetary trajectory solver that calculates a spacecraft route from Earth to Mars, and I am trying to zoom into the spacecraft when it reaches its Mars intercept orbit but am having ...
0
votes
1answer
131 views

Help using NIntegrate

I need some help with NIntegrate. I pasted the code that I wrote below; I know that up to "de" is correct. What I would like to do is NIntegrate de w.r.t phi{0,0.1} and curlE{-10,10}. The final ...
0
votes
0answers
53 views

Ideas for NDSolve?

I'm currently trying to find a numerical solution to a differential equation of the form: D[W[X], {X, 4}] ==(-(1/(delta + G - (G X)/L)^2) + 1/(delta + (G X)/L)^2) ...
3
votes
0answers
55 views

What are good/best practices to take the Fourier transform of an InterpolatingFunction?

I have a function which I have obtained from numerical integration of a differential equation, and I would like to take its Fourier transform. What are good practices for doing this? To make things ...
0
votes
0answers
94 views

Problem with using the results of ParametricNDSolve in a ParametricPlot3D

I new to Mathematica and I have a problem with certain equations. I want to plot a trajectory in spherical coordinates given by the equations: ...
0
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0answers
123 views

A power series expansion

Consider the function, $f(z) = z tanh(\pi z) log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ and ...
0
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0answers
68 views

Solving an ODE, where the coefficients are implicit functions of time, not in closed form [duplicate]

I have an ODE, say of the first order for simplicity, and of the form, $A.x'[t] =B$. The coefficients are functions of time and x[t], not in closed form. I can define the coefficients, $A$ and $B$, ...
0
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1answer
151 views

Numerical integration of two variable function

The aim is to calculate the definite integral of the function $f$ of the form $$f(x,t) \;\;\;\; x \in [0, \infty ) \;\;, \;\;t \in [t_0,T]$$ numerically. For example consider the function below $$f = ...
1
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0answers
50 views

Optimising code for nested integrals

See below for some code I wrote to model a non-homogenous poisson process. The code generates the correct results but takes a long time due to the number of nested integrations. I have tried reducing ...
0
votes
1answer
120 views

Integrand evaluating to non-numerical values

I have solved a system of equations using NDSolve just fine. From there, I can plot the solutions $u(x)$ and $v(x)$, as well as its derivatives, just fine. But, when I want to evaluate the energy ...
1
vote
1answer
41 views

Multiplicate in an Integration with time [closed]

I am calculating the area of a step response. I try to use this Integral Criterion for my Calculation. The time t is multiplicated with the control error xd raised to the second power. ...
1
vote
1answer
174 views

To solve Cylinderical PDE

I want to solve this PDE. I have tried to solve it with NDSolve but found error 'Boundary values may only be specified for one independent variable. Initial ...
1
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1answer
230 views

Multiple plots on same graph for different parameter?

I would like to be able to Plot a function (with an implicit Integrate command) with various values for a certain parameter ...
3
votes
0answers
235 views

Function with a sharp resonance which Mathematica fails to integrate. Why?

I'm a new user of Mathematica and I'm trying to use it to calculate the collisional cross-section as a function of energy for a given potential and decay rate. I know that the resulting function ...
2
votes
2answers
139 views

NIntegrate - WorkingPrecision

I am trying to NIntegrate this expression. It is very close to zero, and so gives all possible types of errors. More precisely, ...
2
votes
2answers
230 views

How can i integrate over a set of data

i need to integrate over my data, which is denoted as {q, I},here I is the Intensity i need to obtain the form of the following integration( its not a numeric integration, because it contain x, next ...
2
votes
1answer
217 views

Area between Contours in ContourPlot

I feel slightly foolish for asking this because I am so close, but I'm having trouble, so I will anyway. I asked this question two days ago regarding finding the lengths of contours. Now, I'd like to ...
0
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1answer
142 views

How to solve this integral equation?

I am trying to solve for x the integral equation : ...
0
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0answers
100 views

an NIntegrate inside a manipulate in mathematica was working and suddenly won't work now. it says indeterminent and it doesn't make any sense why

my title says pretty much everything heres what I'm entering. NumericQ returns a false value but it was true before. Im loosing my patience because this is so ...
3
votes
1answer
202 views

Surface area of intersecting spheres

Given a sphere of radius 1 centered at the origin and $n$ spheres with radii $r_i$ centered at predefined coordinates, $c_i$, in space, I am after the surface area of the unit sphere that is not ...
4
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1answer
251 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...