Questions on the use of numerical functions NIntegrate and NDSolve.

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9
votes
1answer
424 views

Is there a way to see the result of NIntegrate's symbolic preprocessing?

NIntegrate can do a number of different types of symbolic preprocessing on the integrand before starting the numerical calculations, including changes of variables. ...
10
votes
2answers
576 views

Why do I get a different value when I change the order of integration?

I think the following two-dimensional integrals should be equal, since they both integrate the function over the half plane defined by $t>\tau$. $$\int_{-\infty}^\infty \mathrm{d}t \int_{-\infty}^...
5
votes
5answers
1k views

NIntegrate::slwcon Problem

I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate[] needs a lot of time to calculate this. Is there any way to ...
4
votes
1answer
380 views

How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
3
votes
1answer
461 views

A Bessel & Struve functions related integral

I try to numerically compute this integral and I don't figure out why on earth Mathematica is not able to do it. Is my input correct? Does it possibly have a closed form? ...
0
votes
1answer
840 views

How to use NIntegrate in a function using parameters from a list

I would like to use NIntegrate in a function with some parameters from a list. I simplified my problem for this forum. The list of parameters is as follows: ...
0
votes
0answers
165 views

ParametricNDSolve: Parameter inside UnitStep leads to longer integration times

I have found one of the most annoying issues in ParametricNDSolve. When a parameters occurs inside UnitStep (and Piecewise and If) the integration takes much longer time. I illustrate this by an easy ...
3
votes
1answer
817 views

Question on accuracy and precision of NIntegrate

As a Mathematica newbie, I was testing the accuracy/precision of NIntegrate (9.0.1.0 on Mac) and have obtained a very peculiar result. ...
0
votes
0answers
240 views

Differential equation with random variable

How can I derive analytically or compute numerically the solution to following differential equation $$ dy/dt = y\cdot X\cdot (y\cdot X - g(y,X))\cdot X $$ where X is a random variable (e.g. from a ...
0
votes
2answers
313 views

NDSolve boundary query / Extracting values from solution

I have a function $O_{2}$ with boundary conditions $O_{2}(r_{o}) = p_{o} $ and $O_{2}(g) = O_{2}'(g) = 0$. I plot it using the solver code below; ...
2
votes
0answers
291 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
6
votes
2answers
304 views

An integral with a fractional part in 3 dimensions

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
14
votes
1answer
307 views

Inconsistent behavior of WhenEvent[ ]

Consider the following simple example: ...
1
vote
2answers
1k views

Kramers Kronig Relation for Phase and Complex Reflectivity

I am a new user to Mathematica and I have been trying to figure out how to find $\Theta(\omega)$ from my 'experimental' values of energy and $\ln(\sqrt{R(\omega)})$ (I am just running a simulation, ...
1
vote
1answer
2k views

shooting method and stifness problem for NDSolve

I'm trying to solve numerically the following differential equation: 1/r[x]^5 + k/Sqrt[1 + r'[x]^2] - (k r[x]r''[x])/(1 + r'[x]^2)^(3/2) == 0 I can set boundary ...
0
votes
0answers
263 views

NIntegrate with an arbitrary number of variables [duplicate]

I need to evaluate NIntegrate with a variable number of variables. Here's a concrete example. I'll accept an answer that finds a way to make the example work. I ...
10
votes
3answers
1k views

Different results for integration using Mathematica and MATLAB

I have the following integration: $$\text{y}=2 \sqrt{\frac{1}{\pi }} \int_0^{\infty } \frac{e^{-z} \left(1-e^{-\frac{z}{b}} \left(\frac{a}{a+c z}\right)^L\right)}{\sqrt{z}} \, dz$$ I get different ...
0
votes
2answers
249 views

NIntegrate using Boole doesn't work

This doesn't want to work for me - I don't know why not. It usually gives me 0, but sometimes also a different number. I know it should be a small, non-zero number. ...
2
votes
1answer
181 views

Differentiating a function that has NIntegrate within it

I am something of a novice with Mathematica. I have written the following code; ...
0
votes
0answers
70 views

How to solve initial value problem using Runge-Kutta method? [duplicate]

How to solve the following initial value problem using Runge-Kutta method u''[x] + (2/x) u'[x] + E^(u[x]) == 0, u[0] == 0, u'[0] == 0
1
vote
1answer
334 views

Interpolation of a table with 4 parameters

I have a huge data file which I need to do some analysis on it. The file is built in this way that for each 4 variables, there is a value of the function: ...
2
votes
1answer
676 views

Integrate message: can't prove Integration limits are real

I'm working on solving differential equations through Fourier series, I made a function to help me calculate the coefficients that looks like this: ...
0
votes
1answer
229 views

How to improve the performance of this code

I have implemented a code in Mathematica 9 to simulate a scattering problem, and I got really disappointed about its performance when compared to Matlab. Since I am a newbie in Mathematica, would ...
0
votes
1answer
106 views

Transformation of the NDSolve result into new dependent variables

I have solved a set of coupled differential equations and now I need to convert them into different dependent variables and sketch their trajectories. Here is the code I have written so far: ...
1
vote
1answer
170 views

Numerical integration of Hankel functions

I would like to know how to perform numeric integration for the following type of integrals in Mathematica. For the following integrand, we can not get the symbolic result. ...
2
votes
0answers
83 views

ParametricNDSolve and ProcessEquations

I have a question regarding NDSolve`ProcessEquations and ParametricNDSolve. When using the regular NDSolve we have the option to divide the integration into the three steps ProcessEquations, Iterate ...
4
votes
5answers
619 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
0
votes
1answer
664 views

Fitting a Function With a Numerical Integral [duplicate]

I am having trouble using FindFit with the following function. ...
1
vote
0answers
477 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = \frac{1}{...
1
vote
2answers
253 views

PDE plotting assistance needed

...
2
votes
2answers
346 views

Weighted mean of complex exponential function using NIntegrate

I have defined the following functions: ...
9
votes
1answer
1k views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
5
votes
1answer
303 views

Integration of Two Manipulatable Cylinders

Introduction I created the following code to simulate the many possible interactions between a cylindrical protein crystal and a x-ray beam during serial femtosecond crystallography. ...
1
vote
1answer
182 views

Partitioning a numerical integral: need to integrate spectra

I am trying to integrate a spectrum I obtained from a fourier transform infrared spectroscopy experiment, in order to determine the global warming potential of green house gases. In order to do this, ...
1
vote
1answer
221 views

Orthogonalizing polynomials with inner product depending on parameters

I need to orthogonalize the polynomials $h_n(x)=x^{2n}(1+x^2)^{-4S}$ with $x\in\textbf{R}$, $2S\in\textbf{N}$ and $n\in\{1,3,5,\ldots, 4S-1\}$ over the inner product $\langle h_n,h_m\rangle=32\pi S\...
1
vote
1answer
112 views

Two dimensional NIntegration failure - non-numerical values

I've got this function: E0[x0_, y0_, z_]:= A/w[z]*Exp[-(x0^2 + y0^2)/(w[z]*w[z])]*Exp[(I*2*Pi*(x0^2 + y0^2))/(λ*2*R[z])]*Exp[I*ϕ[z]]; Where the ...
5
votes
1answer
705 views

How to improve the solution of a double pendulum system

First, the code: ...
1
vote
1answer
196 views

Manipulating local or external variable within NDSolve

I am wanting to save and use the value of a variable within NDSolve[] but without that variable being part of the equation itself. Code below (ODE for the Leaky ...
7
votes
2answers
398 views

NDSolve Plotting issue

I am trying to solve a system of ODEs with one extra boundary condition. ...
2
votes
0answers
129 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
4
votes
2answers
1k views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
2
votes
2answers
148 views

Definite Integral. Perfomance problem

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral. In Mathematica 4 the result of the following code ...
2
votes
1answer
216 views

Evaluation of the second argument to NIntegrate

The expression Integrate[x^2, Flatten[{{x},{1,2}}]] evaluates properly, to $\frac{7}{3}$. However, ...
1
vote
2answers
365 views

NDSolve - 2nd order ODE - how to solve for y and y'

i am trying to workout how to solve a simple 2nd order ODE for y and y'. I can solve for y[t] as follows but how can i solve for y[t] and y'[t] ? ...
18
votes
4answers
2k views

Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 \leq 1$ in the first octant: ...
6
votes
2answers
217 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...
8
votes
1answer
447 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
6
votes
0answers
130 views

Slow NIntegrate over complicated domains (sometimes)

This is no longer a problem with Mathematica 10.* where I can use regions to do the integrations Overview I have a very large matrix I need to calculate where each element requires the integration ...
1
vote
0answers
193 views

NIntegrate doesn't work

I have a function, Dx[s] (defined in a module) which I can plot: Plot[Dx[s], {s, 0, GetLatticeLength[]}] However if I try ...
1
vote
1answer
1k views

NIntegrate & non-numerical values

I am wondering why I am receiving the message "The integrand ... has evaluated to non-numerical values for all sampling points in the region ..." for a particular calculation I am running. How can I ...