Questions on the use of numerical functions NIntegrate and NDSolve.

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3
votes
1answer
88 views

Surface area of intersecting spheres

Given a sphere of radius 1 centered at the origin and $n$ spheres with radii $r_i$ centered at predefined coordinates, $c_i$, in space, I am after the surface area of the unit sphere that is not ...
1
vote
0answers
36 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
1
vote
0answers
66 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
0
votes
0answers
76 views

Calculating the Lyapunov Exponent/Spectrum for the Duffing Oscillator

Some fellow students and I are trying to calculate and plot the Lyapunov spectrum for the Duffing oscillator (currently a test approach). Each of us has Mathematica knowledge based purely on past ...
0
votes
0answers
66 views

complicated Numerical Integration, FEM application

I am trying to calculate a 2d Integral which has another 2d integral in the integrands. here is the setup: ...
1
vote
0answers
28 views

An example of how to compute numerically the KL-divergence in mathematica [on hold]

I wanted to compute an exact number for two probabilities that I am comparing. These are two normal distributions as: $$Normal(\mu = 5, \sigma = 4)$$ $$Normal(\mu = 5, \sigma = 5)$$ I decided to ...
1
vote
2answers
124 views

Making mathematica do regulated integrals

Consider the integration, $\int _0 ^\infty dx\ x \tanh( \pi x) \sqrt {x^2 + a^2 } $ where $a$ is a real number. This integral is divergent. We note that an asymptotic expansion of the integrand ...
0
votes
0answers
47 views

Numerically Solving Compatible Systems of Overdetermined PDE

Is there an easy way to get Mathematica to numerically solve a compatible system of overdetermined PDE, and plot the solutions? For example, consider the "toy" example $\dfrac{\partial u}{\partial ...
1
vote
0answers
67 views

Imaginary number appears in Integrate [closed]

I had a problem in the following code because when I use Integrate, there will always be imaginary number in the result. I put my code here. The satisfactory result should look like eq 9.138, which I ...
0
votes
1answer
36 views

How can I fix my code so NIntegrate doesn't produce error message?

I get this error when trying to integrate a seemingly simple expression: ...
0
votes
1answer
61 views

Mathematica Compute Time Is Extremely Long (Integrate simple function with parameter scan)

I was wondering if you can help. I have a set of equations I need to solve for a list of parameters; entering each parameter value and solving anew each time is simply not economical. I found a way ...
1
vote
2answers
72 views

NIntegrate piecewise vector function

Is there a way to numerically integrate a vector function defined via Piecewise? Example: ...
1
vote
1answer
71 views

Solution of Coupled Second Order ODEs with Boundary Conditions

D[Tu1[x], {x, 2}] qu - Tu1[x] (fu0 + I w p) == Tou[x] f1 D[T1[x], {x, 2}] q - T1[x] (f0 - b g0 + I w p)== To[x] (f1 - b g1) - g1 For T1 , ...
7
votes
1answer
183 views

Fitting a numerical integral via NonLinearModelFit to magnetic data

I'm new to Mathematica and I'm currently trying to fit $$m_T (H,T) = N_T \int\limits_0^{\infty} \frac{x k_\text{B} T}{\mu_0 H} \mathcal{L}(x) \text{pdf}(D_\text{mag}) \text{d}D_\text{mag}$$ with ...
1
vote
0answers
44 views

How to find out how Mathematica performed an integration? [duplicate]

In terms of integration, I usually utilize Mathematica 9 to compute scattering amplitudes in quantum field theory. Recently, I employed it to compute a particularly difficult integral, and it ...
1
vote
0answers
59 views

Monte Carlo integration with random numbers generated from a Gaussian distribution

I want to do numerical integration of some functions using the Monte Carlo method. The default setting for the Monte Carlo method is to use a uniform distribution as far as I know. How can I change ...
0
votes
1answer
57 views

NDSolve accuracy related problem

I want to solve this equation: ...
0
votes
0answers
69 views

Loop integrals (quantum field theory)

I am attempting to compute the one loop contribution to the Higgs mass, and the one loop integral is somewhat difficult. I decided to try and get Mathematica to do it, to see if the answer can point ...
0
votes
1answer
43 views

Discrete sampling of interpolating function returned by NDSolve

When solving an ODE with NDSolve, Mathematica returns an interpolation function. I need a discrete sampling of this function however. Naively, I can write this as (example): ...
0
votes
0answers
47 views
-2
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0answers
47 views

periodicity of a solution of ndsolve pde

I am solving a pde with NDSolve and the solution is like U(x,t) which seems to be periodic and I am trying to find an algorithm to find the periodicity of such numerical solution. my code is like ...
0
votes
1answer
116 views

I integrate a real function, I want a real result [closed]

I want to count some integral in Mathematica (actually, check that this integral is zero...) I arrive to an answer which has a zero real part but has some imaginary part! Why? This could be a mistake ...
0
votes
0answers
33 views

How does NIntegrate evaluate a piecewise range of x,y?

Could someone explain to me how Mathematica evaluates the following integration. ...
1
vote
1answer
82 views

Problem with numerical integration

I am not very used to do numerical simulations on Mathematica. I have a problem with numerical integration of this function. Is there any way for this calculation? Input: ...
0
votes
0answers
42 views

Boundary Value Problem- using NDSolve or another method

I am trying to solve a set of coupled partial differential equations, with defined boundary conditions using mathematica. Here are the equations and the boundary conditions. ...
1
vote
1answer
74 views

How to calculate the following integral of the multiplication of two Bessel functions?

This integration has an analytical solution and its behavior is described by 1/r^2 function, but Mathematica gives some weird oscillating answer. Can anybody explain this and help me overcome this ...
0
votes
0answers
54 views

Mathematica exit when calling plot. Bug?

I'm currently studing the behaviour of some integral for which I cant find an analytic solution. As this function depend on a vector on the unit sphere, I first defined it with 3 parameters before ...
1
vote
1answer
54 views

NIntegrate(with singularities) gives different results, which one should I trust?

I am doing an Numerical integral with sigularities. ...
1
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0answers
31 views

Integration of any interpolation generates invalid comparison errors [duplicate]

Integrating a simple interpolated function as follows generates invalid comparison errors. ...
0
votes
0answers
51 views

An error message with NIntegrate and inability to plot the integrand

I took a function of x which depended on parameters on m,n,a,y and then first summed up the n from -Infinity to Infinity and then I set the other parameters to some random values and then I asked it ...
5
votes
1answer
84 views

Finding minimum fly-by radius between Mars and spacecraft from interpolating function

I've written an interplanetary trajectory solver/plotter that plots the path taken by a spacecraft on an Earth-Mars mission, but have run into a little trouble when the spacecraft actually reaches ...
1
vote
1answer
42 views

Invariant error plot for an arbitray system of ODE

i try to use InvariantErrorPlot command for a generic system of ODE but i find only example with pre-building equations from Mathematica Packages. This is one of ...
0
votes
0answers
67 views

Integrate double definite integral [duplicate]

I am trying to evaluate an integral numerically and plot its result. My mathematica code is: ...
0
votes
0answers
105 views

Mapping the imaginary axis of the complex (s) plane

In this problem is very difficult to analyze the roots s. Firstly I thought that the problem is in precision, but I am not sure. The criterion which I want to obtain is that one of these roots has a ...
0
votes
0answers
17 views

NDSolve_ODESolve_Plotsolution [duplicate]

I am trying to use mathematica to solve this problem. Thank you! Given the ODE $$ -\frac{a^2 V_0}{2} f''(x)-V_0\cos\big(\frac{2\pi x}{a}\big) f(x)=E f(x) $$ (a,V_0) are positive real constants. Find ...
0
votes
0answers
28 views

trying to speed up sequential use of NDSolve for large system of ODEs

I don't have a basic example just yet but I'll describe the problem for now. I have a large system (>100) of coupled first order ODEs. Where the output from one solution becomes the ICs for the next ...
3
votes
1answer
131 views

Convergence in NIntegrate vs Integrate

I am faced with this situation that for a certain integration, $\int _0 ^\infty \frac { \tanh (\pi \sqrt{x} )} {\sqrt{x+10} } dx$ - the command Integrate returns ...
0
votes
1answer
46 views

Strange result using NIntegrate with Max and PDF

This is really trivial and I appologise in advance if I have made a stupid error somewhere. I have been chasing down some strange results when using NIntegrate with ...
1
vote
1answer
197 views

Euler's method for system of differential equation

I need to program Euler's method to solve a system of two diffferential equations of first order. Fist, I have programmed the Euler's method for just one differential equation: ...
2
votes
1answer
102 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be ...
0
votes
1answer
40 views

NDSolve with arrays and Tables of Equations and WhenEvent

I've been toying around with NDSolve for a while, and read through the website. By doing so I discovered that I could use it for vectors and arrays with much pleasure. So I wanted to write a simple ...
0
votes
1answer
69 views

Multiple NIntegral with singularity

I need to compute the following integral FF[0]. When evaluating FF[0] Mathematica simply takes too much time. The problem may ...
0
votes
1answer
86 views

Initial and boundary value errors

NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> I keep getting this, ...
-5
votes
1answer
83 views

Poincaré section for 3BP

I try to plot the Poincaré section for the 3BP i use the following code that works very well: ...
0
votes
2answers
88 views

How to numerically integrate this integral?

I want to integrate the function funcin (spherical coordinates). ...
1
vote
1answer
52 views

Integrate with FunctionInterpolation differs from NIntegrate

In working with interpolating functions and integration, I noticed a lot of differences between NIntegrate and Integrate in the ...
1
vote
2answers
90 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
3
votes
0answers
79 views

Non-linear integral equation

I'm trying to solve with Mathematica an integral equation. I found this excellent answer (How to solve a non-linear integral equation?) solving with a collocation method a problem which can be ...
10
votes
3answers
601 views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
0
votes
0answers
59 views

Speeding up Integrate and the numerical solution

I want to compute the drag of a plate Below is the code I am using to integrate the function ...