Questions on the use of numerical functions NIntegrate and NDSolve.

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22 views

DerivativeFilter[] is scaling down the data by ~100 or so, not a true differentiation?

I'm running the following function vzz = DerivativeFilter[z["Path"][[All, 2]], {1}]; But if I then integrate vzz the output z is about 100 smaller than the ...
2
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1answer
41 views

How to couple NIntegrate with FindMinValue

I have a problem with a correct transfer of values of parameters when NIntegrate (and some subsequent functions) are coupled with minimizing procedures in ...
2
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2answers
77 views

Reaction-diffusion PDE with NDSolve: either very slow or very inaccurate

I am struggling to have Mathematica 10.3 solve a system of PDE's (with periodic boundary conditions and random initial conditions), but either it produces a set of very noisy InterpolatingFunction ...
0
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0answers
26 views

Integration over n variables and its expression [on hold]

I am having a problem with the following n variable integration and we know $b>0$. $\int ...\int exp \left [-\left ( \sum_{i=1}^{n} x_{i}-an \right )^2 /(2bn) \right ]dx_{1}...dx_{n} $. My goal ...
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1answer
48 views

Multiple stopping constraints in NDSolve

I need to numerically solve several differential equations, with several constraints, like this : ...
-1
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0answers
33 views

Boundary Conditions that depend on each other [on hold]

I have to numerically solve some 4th order differential equations: B''''(r)=f(r,B,B',B'',B''',S,S'), S''(r)=g(r,B,B',S,S') I'm trying to use the shooting method ...
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1answer
41 views

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
1
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1answer
91 views

How to Minimize an NIntegral

My problem is to minimize in Mathematica a numerical integral. The command FindMinimum[With[{R=2.5},NIntegrate[(R*r1*a)*Sin[r1*a],{r1,1,R}]],a] does calculate ...
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0answers
55 views

How to define an exclusion zone for NDSolve

I need to numerically integrate a differential equation and define two exclusion zones to stop the integration. The Mathematica code looks like this : ...
11
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3answers
470 views

Using NDSolve to find particle trajectory

I'm trying to simulate a particle in an electric and magnetic fields, but numerically instead of analytically. This is basically solving the equation $$q \cdot \left(p'\times B\right) + q\cdot E = m ...
1
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1answer
55 views

NIntegrate::inumri: error [closed]

I am getting the following error: NIntegrate::inumri: The integrand c (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- (1+Times[<<2>>])^0.5)) (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- ...
4
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1answer
87 views

System of equations is solved by NDSolve over just a tiny domain

I'm solving numerically a system of differential equations with the use of NDSolve. The numerical integration works only a very small interval of the argument. I'm ...
4
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0answers
50 views

Numerical instabilities of a convection-(non-)diffusion equation when shrinking from a square to a triangular domain

I am trying to evaluate a parameter-dependent indefinite integral using a PDE-based scheme I described here, and I'm having some trouble when I try and cut down the domain from a square to a triangle. ...
4
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1answer
70 views

How can I numerically pre-compute an indefinite integral with a parameter?

Suppose I have a function $f(t)$, and I want to compute its indefinite integral $$F(t)=\int_0^tf(\tau)\mathrm d\tau.$$ Moreover, suppose that, for any of a number of reasons, I require this integral ...
3
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1answer
62 views

Split Boundary Value Problems win Algebraic Equations

Is it possible at all to solve with NDSolve (or other built in function) a split boundary value problem with algebraic equations? Please look at the following example: ...
-3
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0answers
34 views

Integration by using parameter k [duplicate]

I want to calculate the following code by using parameter k. But, the following code provide me no solution. ...
0
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0answers
40 views

Integration by using NDSolve [duplicate]

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
3
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2answers
118 views

How to integrate on bezier function?

I have: points = {{0, 100}, {250, 0}, {0, 300}, {500, 500}} And I want to know the area below the curve, so I came to: ...
2
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1answer
62 views

FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
0
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0answers
35 views

Multiple numerical integrations and green's functions propagation of the solution

I have to solve a system of equations where the coefficients have to be computed from numerical integrations. My problem is that my codes is to extremely slow because I each time that it has to ...
1
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1answer
116 views

NIntegrate (Helium Singlet and Triplet) [closed]

I have two integrals that I am calculating using nested NIntegrate. One is for the singlet helium atom and another for triplet. (here, I am calculating variationally the approximate energies and ...
5
votes
1answer
103 views

Mathematica 10.2 is slow to NIntegrate highly oscillatory integrals

I noticed that Mathematica V10.2 is taking much longer to run my code when compared with V9. One function that seems affected is NIntegrate. For example, for a ...
0
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0answers
29 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
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0answers
15 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
3
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1answer
148 views

Numerically integrate a plotted function

I used Plot[NIntegrate[...]...] to plot a function of 5 different variables. It took really long. Right now I need to integrate this function one more time over the ...
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0answers
53 views

Compiled function and integration

I'm using the recursive functions defined here: MyFnc and myFncC (compiled version). I want to call this functions in the ...
0
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0answers
35 views

Recursions where one definition depends on another. How to Block or have local variables?

I have been using Mathematica to solve a second order differential equation using the second order Verlet method. My code looks like: ...
0
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0answers
25 views

Mathematica AdaptiveQuasiMontecarlo and AdaptiveMontecarlo yield very different results

I'm trying to perform a numerica integral in 5 dimensions. The integral is quite bad behaved, especially in 3 of them, where the integration regions would be [1, infinity]x[0,infinity]x[1,2] but most ...
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2answers
50 views

How can I put a defined symbol as the integrand of NIntegrate, without using a functional form with a pattern test?

Something like this, I define an integrand (really big and hairy, simple below) ...
8
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1answer
63 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
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0answers
32 views

Combining two NDsolves results in “The search has encountered a complex value…” and no solution

So far I used to seperate NDsolves to solve a system of coupled differential equations, where the first NDsolve yields the Boundary conditions for the second NDsolve ...
0
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1answer
55 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
1
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1answer
71 views

Meniscus outside of a cylinder - axisymmetric Young-Laplace equation in semi-infinite domain

How to solve the axisymmetric Young-Laplace equation $$\frac{z'(r)}{r \sqrt{z'(r)^2+1}}+\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}}=z(r)$$ with b.c.s $$z'(1)=-2$$$$z'(\infty)=0$$ where $z=Z/l_c$ ...
0
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0answers
80 views

solving an equation containing an complex integral

I want to solve a numerical equation which include an integral. The problem parameters are : w (is a complex : w = wr +I wi), ...
1
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1answer
28 views

ReleaseHold NIntegrate after Replace variable

I would like to calculate the sum of square of two integral(Ex and Ey). I first hold this two integral because two variables(tx, ty) are not specified.Then, I replace tx,ty and releasehold ...
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0answers
65 views

Solving system of Fredholm integral equations of the second kind

How can we generalize the code previously introduced to solve the Fredholm equation of the second kind to the case of a system of Fredholm integral equations of the second kind? $$ ...
4
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1answer
125 views

Saved InterpolatingFunction behaving badly

Bug introduced in 10 and persists through 10.3.1 or later I created this InterpolatingFunction, and NIntegrate gives an ...
4
votes
2answers
93 views

Derivative before Numerical Integration

I need to take the derivative of a function that have a numerical integration on it. The variable in which the integration will be taken is not the same as the one in which the derivative will be ...
6
votes
2answers
95 views

inspecting step size and order of $\tt NDSolve$

I am trying to collect information about what step sizes and what orders is using NDSolve internally. I tried wrapping it into a ...
1
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0answers
34 views

NIntegrate and Part issues [closed]

I'm trying to numerically evaluate an integral. To try and speed up the process, I decided to calculate some values that will be needed in advance using Parallel Tables. This is what I have: ...
5
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1answer
37 views

Exploiting symmetry makes a 2D NIntegrate harder?

NIntegrate is having trouble converging, for reasons that I don't understand. Here is a simple example. I can compute the area of the curvilinear triangle ...
1
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0answers
169 views

Help with calculating a complicated integral

Edit: The question is solved : )) Thank you for your attention ! I am sorry for mass questions, but the question bothers me a lot. So I would like to ask this question here. This problem arises when ...
4
votes
1answer
91 views

Parametric numerical integration [closed]

I would like to solve the integral: $$ \iiint\frac{e^{-\sqrt{x^2 + k^2}}x^2 \sin{\theta}}{\sqrt{x^2 + k^2}} dx d\theta d\phi$$ defined in $x \in [0,+\infty]$, $\theta \in [0,\pi]$, $\phi \in [0,2 ...
1
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1answer
67 views

How can I combine NIntegrate with NDSolve?

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
0
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2answers
88 views

How can I perform NIntegrate with NDSolve?

I'm a new user and I have no idea how to perform NIntegrate by using NDSolve. For example consider following differential equation (DE): ...
1
vote
0answers
69 views

Problem setting boundary conditions with NDSolve

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu ...
7
votes
1answer
135 views

Numerically evaluating an integral related to Cantor's staircase

Cantor's staircase $F_C(x)$ is a well-known "pathological" function: Plot[CantorStaircase[x], {x, 0, 1}] The MathWorld link given above claims that $$\int_0^1 ...
1
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1answer
70 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by ...
0
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0answers
48 views

NIntegrate some kind of highly oscillatory function

I have an analytical expression (exp) like this, See here. It is a kind of highly oscillatory function for (x1,x2,x3,x4). So,how to get the integral result by ...
0
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0answers
39 views

Order of evaluation for numeric functions

I'm trying to plot a 3D vector field to illustrate an electric field of a uniformly charged disk, and I used Manipulate to change the radius R of the disk to see ...