Questions on the use of numerical functions NIntegrate and NDSolve.

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2answers
43 views

NIntegrate and Integrate of a Spherical Bessel function

I am trying to integrate over a spherical bessel function. I have used both the Integrate and NIntegrate functions in Mathematica but the values given by each do not match. Any reason why this ...
1
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1answer
77 views

How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
2
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1answer
79 views

How to obtain numerical answer for equation containing integration

Could some one tell me how to obtain numerical value of $a$ and $b$ from equations below: $$\frac{1+exp(b)}{1+exp(0.9a+b)}=0.95$$ $$\int_{0}^{\infty} \frac{1+exp(b)}{1+exp(a x+b)}=1$$
4
votes
1answer
232 views

Differentiating ParametricNDSolve solutions

Is there any way to differentiate a solution obtained by ParametricNDSolve? For instance, I have the position $\phi_\gamma(t)$ as a function of time, parametrized ...
1
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1answer
53 views

Finding the true expectation

I have the density function and I want to determine its expected value ...
2
votes
2answers
80 views

WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
3
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0answers
117 views

Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...
0
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0answers
70 views

Numerical Integration/Function

I have a problem with a function defined numerically through an integral of the form: ...
1
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1answer
93 views

Runge-Kutta Butcher tables

I like to have the Butcher's table for Explicit (or implicit as well) Runge-Kutta method of a fixed order. I do not understand reading ...
0
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0answers
27 views

What means the definition F[t_?NumericQ] :=…? [duplicate]

I've come along a function defined in this way: F[t_?NumericQ] := NDSolve[{-u''[x] - u[x]/x == -t^2 u[x], u[x0] == x0, u'[x0] == 1}, u, {x, x0, x1}] What does ...
14
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2answers
182 views

Least effort to handle a point source inside the domain of PDE(s)

By point source I mean a constrained condition at one point inside the domain of PDE(s). For example: $$\frac{\partial ^2u(t,x,y)}{\partial t^2}=\frac{\partial ^2u(t,x,y)}{\partial ...
1
vote
1answer
88 views

Summand is not numerical at some point

I am trying to do some numerical integration with the following codes: ...
0
votes
3answers
69 views

Calculate this integral returns undefined

Limit[ (Integrate[Sqrt[Exp[3 t + 2] + 3] , {t, 0, x}]^2) / Integrate[Sqrt[Exp[6 t - 2] + 5] , {t, 0, x}] , x -> Infinity] This can be solved but ...
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0answers
50 views

Locating Periodic Orbits - Part II

In a previous post Part I I asked how could I locate the x0 position of a periodic orbit. I got only one possible solution but it does not work as I want. Let me be ...
1
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1answer
136 views

Locating Periodic Orbits

Here is the code for the numerical integration of an orbit. First the module for the definition of the equations of motion. ...
4
votes
2answers
158 views

When analytical and numerical methods do not agree - Case study with Maximum Likelihoods methods

Here is the probability distribution I am interested in: $$P(q)=C e^{4 n s q} q^{4 n \nu - 1} (1 - q)^{4 n \mu - 1}$$ , where $e$ is the constant of Euler and $C$ is constant so that the whole thing ...
2
votes
1answer
172 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In ...
6
votes
2answers
129 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...
2
votes
1answer
166 views

Integration of a high oscillatory function

I want to get the numerical result of the integration below: ...
0
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1answer
80 views

InterpolatingFunction used to work with mathematic 7 but not working with mathematica 10

This code is used to work perfectly with Mathematica 7 and now it is not working with Mathematica 10. Any help is appreciated. CL05 = InterpolatingFunction[{{0.5, 11.99999999999999}}, {1, ...
2
votes
2answers
162 views

Plot result of non analytical-integral

I have the following function: h = 1; c = 1; k = 1; B2 = (2*h*c^2)/(x^5 (Exp[(h*c)/(x*k*T)] - 1)); (someone can see that this integral is the Planck function). ...
1
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3answers
74 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
8
votes
1answer
495 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: ...
1
vote
2answers
172 views

NDSolve with Explicit, Implicit Euler and Trapezoidal method

I am using Mathematica 9.0 both on Linux and Windows and I would like to integrate the Van der Pol equation numerically using various techniques such as Explicit and Implicit Euler and Trapezoidal ...
2
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0answers
74 views

Position from 3 dimensional acceleration data? [closed]

Per a previous post on Mathematica StackExchange here I'm trying to utilize 3-axis accelerometer data to determine approximate 3D position. I wanted to start with a simple case. To this end I've ...
1
vote
1answer
74 views

Two dimensional high oscillated numerical integral

I have some problem with two dimensional integral. I want to calculate such integral. ...
2
votes
1answer
46 views

Double application of NIntegrate produces unexpected error messages [duplicate]

In the course of trying to answer 69601, I encountered unexpected error messages. In highly simplified form, NIntegrate[NIntegrate[z y, {y, 0, 10}], {z, 0, 10}] ...
11
votes
3answers
3k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
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1answer
66 views
2
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1answer
111 views

How to use slots and patterns to reduce repetitive calculation?

This is kind of complicated... How can we make MMa calculate values of a function before doing multiple pattern or slot substitutions? Answers to similar questions didn't cover the case where the ...
1
vote
2answers
55 views

Incomplete Integration in Area

Area[2 Sqrt[(1 - p^2)^2 - r^2], {p, 0, 1}, {r, 0, 1 - p^2}] is able to perform only the integral over r, leaving the integral ...
0
votes
1answer
42 views

NIntegrate with units: unable to determine the units of quanitites that appear in the input

I want to integrate Planck's law of radiation in a certain wavelength intervall with units. I define some constants: ...
3
votes
1answer
95 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 ...
4
votes
1answer
251 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: ...
9
votes
1answer
173 views

Is this a bug in NIntegrate?

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 answer for the same ...
1
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0answers
49 views

Numerical integration with symbolic coefficients

Thanks to Michael and its reply here I managed to deal with some of the more complicated integrals. But still there are some even more complicated ones. Let give a specific example. ...
2
votes
2answers
77 views

FindFit working with Integrate but not NIntegrate - I am using “?NumericQ”

I'm having some syntax problems with finding a fit to an equation that doesn't have an analytical expression for it's integral. Because I think the problem is one of syntax, I am substituting a ...
1
vote
1answer
51 views

numerical integration question

The actual expressions is quite complicated so I will use a trivial example. Let In[36]:= f[u_] := 1/3 - (5/18)*(Cos[u]*a[1] + Sin[u]*b[1])^2 Then ...
0
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0answers
35 views

Order of evaluation when using Solve and Minimize

I have to solve numerically an integral, that ends up being more or less as follows: Solve[f[x]==a*Sum[Sin[x-i]*(f[i]-f[i-1]),{i,1,x}],f[x]] (not actual ...
-3
votes
1answer
104 views

Integration with mathematica? [closed]

I am very new to Mathematica. I am trying to evaluate ∫ (1+lnx)Sqrt(1+(xlnx)^2) using Mathematica. I know a substitution must be done so I have set ...
1
vote
1answer
24 views

NIntegrate is it possible to evaluate the integral using a user-defined grid?

I am using the NIntegrate function and I would like Mathematica to perform the integration in accordance with a grid I define that is sampled uniformly between the boundaries of integration. Let me ...
0
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1answer
44 views
2
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1answer
58 views

NIntegrate and Interval regions

NIntegrate does not seem to like Intervals as regions. Consider the following example function defined for a parameter "a" ...
4
votes
1answer
191 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 ...
0
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1answer
75 views
1
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2answers
69 views
3
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1answer
83 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 ...