Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

1
vote
1answer
40 views

NIntegrate::inumri: error [on hold]

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
votes
1answer
78 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
votes
0answers
47 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. ...
3
votes
1answer
64 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
votes
1answer
56 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
votes
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
votes
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
votes
2answers
115 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
votes
1answer
58 views

FindRoot of interpolating function from NDSolve

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

How to numerically integrate a multi-dimensional gaussian times a polynomial? [closed]

I'm trying to use NIntegrate on an equation of the form \begin{eqnarray} \mathrm{Poly}_{4}(P_{1},P_{2},Q_{1},Q_{2})\mathrm{Exp}(-\mathrm{Poly}_{2}(P_{1},P_{2},Q_{1},Q_{2})) \end{eqnarray} Where ...
0
votes
0answers
26 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
vote
1answer
113 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
101 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
votes
0answers
28 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 ...
0
votes
0answers
15 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
3
votes
1answer
146 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 ...
1
vote
0answers
52 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
votes
0answers
34 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
votes
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 ...
0
votes
0answers
28 views

NDSolve Method Plugin Framework for the Explicit Modified Midpoint method

I'm trying to implement the Explicit Modified Midpoint method as a base for the Extrapolation method using NDSolve Method Plugin Framework for the comparison with the built-in one. The bottleneck in ...
0
votes
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) ...
6
votes
0answers
47 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
0
votes
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
votes
1answer
54 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
1
vote
1answer
70 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
votes
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
vote
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 ...
0
votes
0answers
64 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
votes
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
92 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
94 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
vote
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
votes
1answer
36 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
vote
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
vote
1answer
66 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
votes
2answers
78 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
65 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
134 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
vote
1answer
64 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
votes
0answers
47 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
votes
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 ...
0
votes
0answers
48 views

Integration with a sharp peak

This question is related to my previous question: Avoid Evaluation of Function at NDSolve I have a function which behaves like in the following figures: These graphs are cuts from an interval. My ...
0
votes
2answers
60 views

NIntegrate problem with limits in triple integral [closed]

So I am trying to solve a triple integral in mathematica, but I am getting errors regarding my limits of integration. This is my code: ...
1
vote
1answer
340 views

How to code the following in Mathematica

How do I get the following into Mathematica, solving for a: $$ 0.7 = 1 - \frac{2}{a} \times [ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1} dx + \frac{a}{6} - 1] $$
0
votes
0answers
48 views

Time needed to solve NIntegrate is much longer than what I was expecting

I'm trying to do the following list: tablevdip = ParallelTable[{x, y, Vdip[x, y, 6]}, {x, -1, 1, .5}, {y, -1, 1, .5}];] with ...
3
votes
0answers
54 views

Avoid Evaluation of Function at NDSolve

I have a huge "black-box" f function, which I want to integrate. Let's define it: f[x_,y_,a_]:=a*Exp[-(a*10000)(x^3+y^3)] as ...
0
votes
1answer
72 views

Integrating high oscillatory function - triple integral - error message

I am working in a triple integral, but the second integral (qQ) and the first too ( aA ) is a oscillatory funcion. The third integral ( os11 ) is like a gaussian, and is easy to integrate. i am ...
2
votes
2answers
101 views

Solving nonlinear 3rd order ODE over range from zero to infinity

Here are the code that I had tried but there is an error ...
0
votes
1answer
164 views

Plotting singular integral

I need to plot the following singular double integration $u(x,t)$ for $t=0, t=0.2, t=0.4, t=1$ and $t=2$ in one figure as a line. That is, I need $u$-coordinate vertically and $x$-coordinate ...