Questions on the use of numerical functions NIntegrate and NDSolve.

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2
votes
0answers
121 views

Global vs local adaptive integration: lattice propagator

I was doing the first exercise in the paper Lattice QCD for Novices. This is the expected result: With the default "GlobalAdaptive" method for NIntegrate it threw errors saying that the error had ...
1
vote
0answers
106 views

Choosing PrecissionGoal and AccuracyGoal for decomposed integral with NIntegrate

Assume I have a complicated integral $I$ which can feature all kinds of difficulties like infinite interval, rapidly oscillatory integrand, integrable singularities and numerically almost singular ...
3
votes
1answer
276 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? ...
1
vote
3answers
460 views

Solve for variable in integral limit when using NIntegrate

I am trying to solve for a variable which appears in the limits of an integral, rather like in the following; ...
7
votes
2answers
252 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 ...
1
vote
0answers
230 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
0
votes
0answers
84 views

Convergence problems with numerical integration of specific functions

I want to numerically integrate two functions that have several poles inside the integration region. These are the functions: ...
4
votes
1answer
205 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 ...
7
votes
1answer
241 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. ...
0
votes
1answer
100 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: ...
4
votes
5answers
331 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 ...
0
votes
1answer
187 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
73 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 ...
2
votes
1answer
213 views

How to use NIntegrate in a purely numerical mode?

I have a function that is defined as the smallest root of a given polynomial. Something like this: ...
0
votes
0answers
60 views

PDE syntax question

I am trying to solve a PDE of a reaction diffusion equation, and while I'm getting a decent looking solution, I am also getting inconsistent BC / initial conditions warnings and wanted to check if my ...
8
votes
4answers
370 views

NIntegrate extremely piecewised functions

I often need to integrate extremely piecewised functions, like the following one (not extreme, but gives an idea): ...
0
votes
0answers
103 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 ...
2
votes
0answers
108 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
0
votes
2answers
461 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, ...
5
votes
2answers
191 views

Triple fractional part-related integral

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
18
votes
4answers
1k views

How to integrate functions of linearly interpolated data?

At first, consider integration of pure InterpolatingFunction. Importing some data (works in v.9, for earlier versions one can use this link to download zipped ...
6
votes
2answers
1k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
0
votes
0answers
95 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 ...
9
votes
3answers
564 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
137 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. ...
4
votes
5answers
389 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 ...
7
votes
0answers
381 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: ...
2
votes
1answer
80 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
58 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
2
votes
1answer
213 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
182 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 ...
1
vote
0answers
238 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} = ...
1
vote
1answer
107 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. ...
0
votes
0answers
76 views

Error Interpretation with NIntegrate, max. possible accuracy/precision

I guess the right question to this is: Which method is used at NIntegrate with Mathematica 8 as default and which is used with Mathematica 9 as default? ...
1
vote
0answers
51 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 ...
5
votes
1answer
201 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. ...
0
votes
1answer
211 views

Fitting a Function With a Numerical Integral [duplicate]

I am having trouble using FindFit with the following function. ...
0
votes
1answer
93 views
2
votes
2answers
198 views
6
votes
2answers
336 views

NDSolve Plotting issue

I am trying to solve a system of ODEs with one extra boundary condition. ...
1
vote
1answer
122 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, ...
4
votes
0answers
302 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a pieceise function. If we define the ODE system ...
1
vote
1answer
72 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 ...
1
vote
1answer
114 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 ...
7
votes
1answer
410 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) ...
0
votes
0answers
88 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 ...
2
votes
0answers
90 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: ...
2
votes
2answers
114 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 ...
1
vote
2answers
137 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] ? ...