Questions on the use of numerical functions NIntegrate and NDSolve.

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2
votes
1answer
162 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
137 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
972 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
3
votes
2answers
485 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
127 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
172 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
159 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
94 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
129 views

Using `N` gives strange result

Consider these two functions which are almost the same: ...
0
votes
0answers
102 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
171 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
90 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
188 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
114 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
80 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
81 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
132 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
108 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 ...
1
vote
2answers
125 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
193 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
61 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?
1
vote
1answer
142 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
140 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
102 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
1
vote
1answer
139 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
515 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
123 views

NIntegrate:eincr error

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

NIntegrate Error

I am trying to solve this expression with the function NIntegrate: ...
3
votes
2answers
344 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
337 views
2
votes
0answers
149 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
267 views

2-Dimensional NFourierTransform

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

Numerical Integration

I have used the following code to evaluate an integral (val) numerically ...
3
votes
0answers
361 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: ...
8
votes
2answers
170 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
138 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
277 views

NDSolve giving the wrong solution?

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

How do I perform the following numerical integration [duplicate]

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
120 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 ...
5
votes
1answer
236 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 ; ...
10
votes
2answers
465 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 ...
4
votes
3answers
742 views

Find arc length

I am trying to find the arc length for using ...
5
votes
1answer
117 views

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to ...
1
vote
2answers
253 views

Integrating Squared of Interpolating Function with respect to one variable

I am interested in evaluating a two dimensional interpolating function produced by solving the wave equation. Here is the code that includes the resulting interpolating function. ...
0
votes
0answers
47 views

Getting message NIntegrate::inumr: in V10; did not happen in V9 [duplicate]

I just tried making a ParametricPlot that worked error-free in Mathematica 9, but now produces errors before successfully plotting in Mathematica 10. It appears to ...
4
votes
0answers
66 views

NIntegrate::ncvbr: How should we interpret and handle this error not mentioned in any documentation?

I have some user-defined module describing my integrand which has to be computed numerically (it's much more complicated than this but bear with me): ...
2
votes
2answers
152 views

Improving convergence in a numerical integration (Version 5.2)

I have a double integral that I am trying to calculate numerically, and I'm having convergence issues. ...
0
votes
0answers
191 views

How can one use differential boundary conditions with helmholzSolve?

I can not get the helmholzSolve function provided by Mark McClure and user21 to work for a case that I want to constrain the spacial derivative of a boundary. In ...
10
votes
1answer
238 views

Is this a bug in NIntegrate?

Fixed in 10.1 Bug is present as of version 10.0.2 checked on windows 7, 64 bit Is this a bug or I missed something? NIntegrate seems to give a different ...