Questions on the use of numerical functions NIntegrate and NDSolve.

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3
votes
1answer
68 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
44 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
61 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
52 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): ...
1
vote
1answer
879 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
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
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 ...
4
votes
1answer
647 views

Tips for efficiently solving large system coupled (nonlinear) ODEs

I'm trying to solve a system of nonlinear, coupled ODEs, where the governing equation for the $n$-th ODE is of the form: $$\sum_k^M Q_{nk} \ddot{a}_k -\sum_{\ell}^M\sum_k^M S_n(\ell,k) ...
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 ...
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 ...
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 ...
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 ...
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 ...
0
votes
0answers
15 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
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
2answers
50 views
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
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 ...
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
1answer
54 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
1
vote
1answer
69 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 $z=Z/l_c$ ...
6
votes
2answers
280 views

An integral with a fractional part in 3 dimensions

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
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): ...
3
votes
1answer
354 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
0
votes
1answer
204 views

Existence of an analytical form for integral

Can the following integration be performed with an analytical output? ...
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? $$ ...
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
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
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 ...
7
votes
0answers
515 views

Modelling Hysteresis with a Differential Equation

I want to implement the bulk ferromagnetic hysteresis model (mostly the Jiles-Atherton Model), see http://drum.lib.umd.edu/bitstream/1903/6043/1/PhD_99-1.pdf page 44 equation (30). The needed ...
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 ...
10
votes
2answers
408 views

Symbolic integration fails while numerical integration succeeds

I am hoping to evaluate the following integral Integrate[((r^3 - 7)^(2/3)*(1 - (r^3 - 7)^(2/3)/r^2))/r^3, {r, 2, Infinity}] but Mathematica informs me that this ...
5
votes
1answer
258 views

Obtaining an NIntegrate error estimate

Is there a way to extract the error that Mathematica estimates when calculating a numerical integral using NIntegrate? Internally Mathematica must keep track of ...
3
votes
1answer
78 views

Want NIntegrate to catch error message

Really stuck with this. When I use NIntegrate, it sometimes prints a message like NIntegrate::ncvb: "NIntegrate failed to converge to prescribed accuracy ...
6
votes
1answer
810 views
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: ...
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: ...
0
votes
1answer
100 views

How to limit the number of plot points [closed]

I'm using Mathematica to plot a function that has been defined in the following way: ...
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 ...
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
0answers
73 views

Passing integration constants to self defined function

I would like to evaluate an integral I am taking in cylindrical coordinates, in which the integrand contains a previously defined function. I need to pass the r and phi integrand values to this ...