Questions on the use of numerical functions NIntegrate and NDSolve.

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6
votes
1answer
112 views

How do I extract the weights used by NIntegrate?

I'd like to use NIntegrate to adaptively integrate an expression, then use the same points and weights to integrate that expression with some parameters changed. I ...
3
votes
0answers
112 views

Implementing the Numerov method for solving ODEs with NDSolve

I'd like to implement the Numerov scheme for solving an ODE (Scroedinger Eq time-independent) with NDSolve. I tried in analogy with the Runge Kutta example in the ...
1
vote
1answer
81 views

NIntegrate discrepancies

I want to compute a numerical integral for a gaussian trivariate distribution. Say ...
5
votes
2answers
103 views

Convergence data for Monte Carlo NIntegrate

I am using NIntegrate with Method -> "MonteCarlo" to evaluate a high dimensional integral. Is there a way I can obtain a list ...
0
votes
1answer
110 views

Is it possible to get the exact value of the integration?

I have the following code in Mathematica. ...
1
vote
2answers
69 views

Export NDSolve data

I have calculated a solution of a system of differential equations using NDSolve and generated a plot. How could I extract the data of the solutions? The input is ...
0
votes
0answers
41 views

How to solve equation which has three variables and integration?

My equation is in the form x^2+y^2+50[Integrate[Exp[-P^2/10]*Log[(x + y*p + 1)/(x - y*p - 1)],{p,0,100} The range of x and <...
1
vote
0answers
56 views

NIntegration and DSolve with same variable

I need to solve this problem: Then follows the code, with: ...
7
votes
2answers
340 views

Plotting the image of a curve under a flow

I have some explicit time-independent vector field on the plane, and I would like to study how points evolve under the flow generated by this vector field. The flow is rather complicated and cannot be ...
3
votes
4answers
308 views

Using NIntegrate to integrate functions with sharp peaks (Lorentzian-like)

I have a problem with NIntegrate that I do not understand. I want to integrate a function f[x], which has a complicated analytic ...
5
votes
2answers
123 views

Why is NDSolve's StartingStepSize with ExplicitEuler not working? How do I set the step size?

Why do I get a smooth curve (that is obviously wrong) when I run this? ...
1
vote
0answers
37 views

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

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
votes
1answer
48 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 ...
3
votes
2answers
130 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
votes
1answer
60 views

Multiple stopping constraints in NDSolve

I need to numerically solve several differential equations, with several constraints, like this : ...
1
vote
1answer
50 views

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
1
vote
1answer
125 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 ...
0
votes
0answers
64 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 : ...
12
votes
3answers
539 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
vote
1answer
78 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
votes
1answer
100 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
65 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
votes
1answer
83 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
75 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: ...
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): ...
5
votes
3answers
212 views

How to integrate a Bézier 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
128 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
42 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
134 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
200 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
35 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
16 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
3
votes
1answer
194 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
73 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
39 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
37 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
2answers
70 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) ...
9
votes
1answer
76 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
0
votes
0answers
49 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
71 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
3
votes
1answer
124 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
91 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), <...
2
votes
1answer
46 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 $Ex^2+Ey^2$....
0
votes
0answers
101 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? $$ f_{1}(x)-\lambda_{...
4
votes
1answer
131 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
102 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 ...
7
votes
2answers
127 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
46 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
50 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
175 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 ...