Questions on the use of numerical functions NIntegrate and NDSolve.

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0
votes
1answer
41 views

Different results for NIntegrate for the same function using cartesian and polar coordinates

This is probably a straightforward question. I have two functions f[x_,y_,z_] and g[r_, theta_, z_] where: g[r_, theta_, z_] returns f[ r Cos[theta], r Sin[theta], z]. For the same points in ...
2
votes
1answer
79 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
1
vote
1answer
58 views

Increase Precision in Numerical Integration

I need to generate a table of Chebyshev expansion coefficients of trigonometric functions (in this case Cos[2 Pi t] to very high accuracy. Code is: ...
3
votes
1answer
205 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
3
votes
1answer
190 views

How to numerically integrate this integral

I am unable to do this definite integral in Mathematica 9. Is there any command so that I can get the numerical value of the above integration? Code: ...
-1
votes
1answer
42 views

Numerical integration of modified bessel function

I try to numerically compute this integral but I receive many errors and I end up getting unreasonable answers, I know that there's a closed form answer but I have to compute it numerically. Would ...
0
votes
0answers
78 views

“General” strategy to use NIntegrate for multidimension integrals?

I don't have much experience of numerical methods for multidimensional integrals. Currently, the particular function I want to integrate is: $$f(x,y,z,p_x,p_y,p_z) = \frac{p_x^2(2 p_x x(p_y y + 4 p_z ...
5
votes
2answers
98 views

How to add (energy) constraint when using NDSolve to Equation of Motion

To simplify my problem, I will try and solve the Equation of Motion for a particle in a 1D Harmonic Potential. energy[x_, p_, m_, ω_] := p^2/(2 m) + (m ω^2)/2 x^2 ...
0
votes
1answer
59 views

Multidimensional NIntegrate problem of the function decaying as 1/x^2

The function I am trying to integrate is more complicated but I can simply write the function as (I had made a typo error, sorry. The '+' sign in front of the r should be '-'): $f(\omega ) = \int ...
4
votes
1answer
105 views

Using `N` gives strange result

Consider these two functions which are almost the same: ...
0
votes
0answers
78 views

Unequal behaviour of FindRoot to two similar functions

Unfortunately, I have some difficulties to plot a function. Here is my code: ...
1
vote
0answers
37 views

Using real numbers gives suspicious result

In the code below when I use a real number for number 4 in the exponent in the irf function, it returns wrong result. ...
4
votes
2answers
134 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
3
votes
1answer
69 views

NIntegrate on tetrahedron

I've been trying to numerically calculate an integral in a tetrahedron of a discretized domain. In some cases when I specify a method I've been getting the error message NIntegrate::femonly ...
0
votes
0answers
34 views

How to tell NDSolve to ignore small values in choosing step size

I have a very large system of first order differential equations, which can be written (on paper) as dX/dt=F(X), where X is a vector and F is a vector function. All elements of X are strictly positive ...
0
votes
0answers
56 views

Mathematica Integrate implicit assumptions returns a function not defined in some points while NIntegrate performs integration safely

Hi guys i'm performing a standard integration with mathematica routine Integrate, the function i'm integrating is the following: ...
0
votes
0answers
62 views

Plotting a Function that contains a Numerical Integration

I'm using mathematica to plot a function that has been defined in the following way: ...
1
vote
1answer
74 views

Mathematica multi-dimensional numerical integration default method

I'm performing multidimensional Numerical integrations with mathematica I was wondering what was the default method that mathematica was using. Also i'm changing some parameter inside the integration, ...
1
vote
1answer
66 views

Strange integration

I tried to evaluate this line Integrate[((-I/2) (E^((-I) x) - E^(I x)) + ((E^((-I) x) + E^(I x)) x)/ 2)/((-1 + E^x) x), {x, 0, Infinity}] Then I get $14$ ...
1
vote
0answers
30 views

Can NIntegrate be used with the Levin method in several dimensions?

I've got some data in the form of an interpolating function. It's a function of three variables, $\rho(x,y,z)$. I'd basically like to integrate this with some phase over a cube of known size, like $$ ...
0
votes
1answer
40 views

Error messages from NIntegrate [closed]

I've been trying to work on some integrals (Actuarial Science, for those interested) but somehow this always returns an error for me. ...
1
vote
0answers
74 views

Numerical solution to two non-linear coupled differential equations [closed]

I am trying to solve two differential equations representing the position of an object in space. I have specified arbitrary initial conditions. ...
3
votes
0answers
55 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the follwoing integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, Infinity}, Assumptions -> z \[Element] Reals] >> -3.36354 - 3.85013 I the ...
1
vote
0answers
58 views

Problems with NIntegrate, levmaxord error

I am trying to integrate some spherical harmonics, for scattering over a sphere, using the SphericalHarmonicY and NIntegrate ...
0
votes
0answers
55 views

Numerical integration with large exponents

To make a long story short, I am doing mostly analytic calculations and therefore do note have good skills in numerical integration. I have to numerical integrate the following integral ...
2
votes
1answer
133 views

2D Fourier transform of a few (4) disjoint discs on a plane

I'd really appreciate some advice. Short Version I'm trying to calculate the following $$ ...
2
votes
0answers
48 views

Number recognition in Mathematica [closed]

Suppose that I have a number $n$ with many decimal digits of precision. What is the code to use to get Mathematica to recognize possible closed-form expressions for that number?
0
votes
1answer
81 views

How to compute an integral with 300 digits accuracy [closed]

I'm new to Mathematica and I would like to ask what is the code to use to calculate numerically an integral with 300 digits precision; also, I would like to know what is the right code to use the ...
1
vote
1answer
81 views

Computer freezes during NIntegrate[]

I have a notebook that freezes the computer every time I run it (I mean the whole computer becomes unresponsive and do not react to ctrl-shift-esc and ctr-alt-delete as well as alt-tab and ...
1
vote
0answers
72 views

PDE with Integral constraint

I am trying to solve the Non-linear Schrodinger equation $-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$ In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times ...
2
votes
1answer
85 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
1
vote
1answer
81 views

How to evaluate complex numerical integral in mathematica?

I have an integral of the form \begin{align} F(\omega) = \int_0^{\infty} f(s,\omega) \mathrm{d}s \end{align} which I would like to numerically evaluate and plot for a range of $\omega \in ...
1
vote
1answer
153 views

Solving Fredholm Equation of the first kind [duplicate]

I want to numerically solve Fredholm integral equations of the first kind, equations of the form $$g(t)=\int_a^b K(t,s)f(s)\,\mathrm{d}s$$ where we know the functions $K(t,s)$ and $g(t)$ and seek to ...
0
votes
1answer
82 views

NIntegrate:eincr error

I am trying to solve this expression in Mathematica with the function NIntegrate: ...
0
votes
2answers
77 views

NIntegrate Error

I am trying to solve this expression with the function NIntegrate: ...
3
votes
2answers
110 views

NIntegrate giving message NIntegrate::slwcon:

I got this interesting answer from Mathematica when trying to integrate my function numerically: f[x_] := Sqrt[17*x^2 + x^4] NIntegrate[f[x], {x, -1, 2}] ...
1
vote
1answer
115 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
3
votes
4answers
197 views
2
votes
0answers
93 views

Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
2
votes
1answer
162 views

2-Dimensional NFourierTransform

Mathematica FourierSeries package contains the NFourierTransform function for calculating 1-D Fourier integral numerically. ...
0
votes
2answers
93 views

Numerical Integration

I have used the following code to evaluate an integral (val) numerically ...
2
votes
0answers
151 views

Solve integral equation for upper bound

I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: ...
7
votes
2answers
154 views

Efficient way to obtain values of a function defined by an Integral

Consider the following equation: $$S(q)=\frac{(4 \pi \rho ) \int r (h(r)-1) \sin (q r) \, dr}{q}$$ I want to numerically obtain values for $S(q)$ given that I have data points representing $h(r)$ ...
3
votes
1answer
94 views

Calculate the relationship between the duration of two oscillating functions

I am trying to quantitatively determine the relationship between the length of two oscillating functions. Meaning, what is the duration of the green spike in relation to the blue square? Does anyone ...
1
vote
1answer
135 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
0
votes
0answers
83 views

How do I perform the following numerical integration

I have the following integral to evaluate numerically: $$x(t) = \frac{1}{f(t)}\int_0^{t_b} t^m (t + n)^o \sin(pt) \mathrm{d}t \quad m,n,o,p \in \mathbb{R}$$ ...
4
votes
1answer
82 views

Possible bug / numerical issues with HypergeometricU — any suggestions for a fast workaround?

I've encountered some problematic behaviour with HypergeometricU. I have a probability distribution on the positive integers that takes the following form after ...
4
votes
1answer
143 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; ...
7
votes
2answers
224 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns several error messages: ...