Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

0
votes
1answer
82 views

nintegrate: greater accuracy possible

I've got the following piece of code: ...
3
votes
1answer
173 views

NIntegrate and Interval regions

NIntegrate does not seem to like Intervals as regions. Consider the following example function defined for a parameter "a" ...
5
votes
1answer
408 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
1
vote
2answers
145 views

Output of NIntegrate depends on MaxRecursion

I have an integral in this form: ...
3
votes
1answer
211 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
2
votes
0answers
196 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
4
votes
2answers
301 views

How to plot a function that is not defined after certain point

I'm plotting a function that I get after numerically integrating over another function. Something like: f[x_,y_]:=NIntegrate[g[x,y,z],{z,0,1}] I know that above ...
1
vote
1answer
951 views

First::normal: Nonatomic expression expected at position 1 in First[0]. >>

I'm trying to do a numerical integration. The integration is within a function. ...
2
votes
1answer
361 views

Catastrophic loss of precision

I am trying to solve a double integral in the range of 0 to Infinity (for both the integrals) and Mathematica is giving me the following error: Catastrophic loss of precision in the global error ...
9
votes
4answers
606 views

Calculating an integral by the Romberg Algorithm

In my "Numerical Analysis" course, I learned the Romberg Algorithm to numerically calculate the integral. The Romberg Algorithm as shown below: $$T_{2n}(f)+\frac{1}{4^1-1}[T_{2n}(f)-T_{n}(f)]=...
1
vote
0answers
106 views

Is there any way to solve this convex-concave like optimization problem?

This is a bit of a non-standard way of asking a question perhaps but I couldnt even think of writing any code about the following optimization problem. I wonder if it could be at all solvable and if ...
4
votes
1answer
215 views

How to evaluate differential entropy from raw data?

I want to evaluate the differential entropy according to here $$h(X) = - \int f(x) \log{f(x)} dx$$ where $f$ is the probability density function. Lets create some test data (normal distribution): <...
1
vote
0answers
56 views

Is it possible to pipe the output of EvaluationMonitor to Excel?

I have an EvaluationMonitor setup to capture the points processed by NIntegrate. This is a case where the same function, integrated over the same region in cartesian coordinates yields a dramatically ...
0
votes
1answer
92 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
207 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
172 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: ...
4
votes
1answer
1k views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
3
votes
2answers
615 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
vote
2answers
153 views

Numerical integration of modified bessel function

I need to compute the following integral: NIntegrate[ BesselI[-nu, k x]/x ,{x, r1, r}] in which nu=-(2m-1)/2 and I have to ...
0
votes
0answers
202 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
177 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
105 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
137 views

Using `N` gives strange result

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

Unequal behaviour of FindRoot to two similar functions

Unfortunately, I have some difficulties to plot a function. Here is my code: ...
4
votes
2answers
187 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
100 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 <...
1
vote
1answer
209 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, ...
3
votes
1answer
121 views

Strange integration

Bug introduced in 9.0 or earlier and fixed in 10.1 Note: Beginning with V10.1, this integral returns unevaluated but without error messages. I tried to evaluate this line ...
1
vote
0answers
105 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 $$ ...
4
votes
0answers
88 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
159 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
118 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 $$\int_{a_1}^...
1
vote
2answers
147 views

Plot3D and NIntegrate issues

f[x_, y_] := 2*x - y Plot3D[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] NIntegrate[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] I ...
2
votes
1answer
214 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 $$ \psi(X,Y,z=d)=\underset{aperature}{\iint}\psi(x,y,z=0)e^{-i\frac{k}{d}\left(xX+yY\right)}dxdy\\\psi(x,y,z=0)=...
1
vote
1answer
159 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 windows-tab)...
1
vote
0answers
175 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 [0,...
2
votes
1answer
103 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
1
vote
1answer
166 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 $\omega \in [-30,30]$...
1
vote
1answer
610 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
138 views

NIntegrate:eincr error

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

NIntegrate Error

I am trying to solve this expression with the function NIntegrate: ...
3
votes
2answers
473 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}] ...
3
votes
4answers
425 views
2
votes
0answers
160 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
311 views

2-Dimensional NFourierTransform

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

Numerical Integration

I have used the following code to evaluate an integral (val) numerically ...
4
votes
0answers
415 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: f[t_] = Sqrt[1 + E^(-2 t)] ...
9
votes
2answers
182 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
147 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 ...