Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

0
votes
1answer
86 views

difficulty in numerical estimate of double integral

I entered the following simple integral in mathematica: ...
0
votes
1answer
64 views

Why does Mathematica 10.3.1 fail me on : Integrate[(x^3) [Log[2 Sin[x]]]^8, {x, 0, Pi}] [closed]

All it gives me is a pretty restatement of my original request. When I use WolframAlpha PRO, I get a result of 624510 and a visual representation of the area in question. I know the ends of the ...
10
votes
0answers
135 views

Strange behaviour of integrals with Cos, Sin, and Exp

During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would consider it a bug. ...
4
votes
3answers
189 views

How to solve this integration? [closed]

I need to find the integration of the following expression ...
1
vote
1answer
68 views

numerical integration over divergence

Consider the following function g1: ...
2
votes
1answer
155 views

The numerical solution of a nonlinear ODE: boundary value problem

I want to solve the following nonlinear ordinary differential equation with boundary values $f(0)=1$ and $f(1)=1$: $${\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left( x \right) ={\dfrac { \left( 51-51\,x ...
3
votes
3answers
63 views

Replace variable with value prior to evaluating NIntegrate

The title says it all. Reading posts such as this however, I'm not seeing how to do this. This is the simplest example that can show my problem. ...
2
votes
1answer
49 views

Numerical Integration with absolute value [duplicate]

I want to find the area enclosed by the fourth heart curve (http://www.wolframalpha.com/input/?i=fourth+heart+curve). Since both $y(t)$ and $x(t)$ are given and I know that $t$ is in the range ...
0
votes
0answers
60 views

Another question about inverse Laplace transform

Given $r = 0.06;\quad \theta = 105;\quad \kappa = 1;\quad x_0 = 100;\quad K = 100;\quad \sigma = 0.10;\quad T = 0.25;$ Define $ \nu = -\kappa/\sigma^2 - 0.5;\quad p = \kappa*\theta/\sigma;\quad q = ...
0
votes
0answers
23 views

Nested Numerical Integration [duplicate]

So I am trying to evalute the following Integral Numerically: $$\int_{\mathcal{J}^+(x_0)\cap\mathcal{J}^-(x_f)}^{}A(x_0,x_1)\int_{\mathcal{J}^+(x_1)\cap\mathcal{J}^-(x_f)}^{}A(x_1,x_2) dx_1dx_2$$ ...
2
votes
2answers
91 views

How to find the integrand singularity points when having NIntegrate::slwcon:

In order to calculate the closed area of the curve below defined by parametric equation curve02, ...
3
votes
1answer
45 views

My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
0
votes
1answer
46 views

ND on a function using NIntegrate

I need to numerically differentiate a function that takes a list as an argument and that uses NIntegrate in its definition. A simple example is ...
1
vote
0answers
41 views

Numerical Integral with Boolean as part of argument

I am trying to numerically calculate a partial surface area integral of an oblate spheroid in spherical coordinates. The area I want to calculate is determined by a boolean function in the argument of ...
3
votes
0answers
55 views

Singularity treatment in a simple problem [duplicate]

With a simple search, several posts can be found on treating singularities encountered while using NDSolvefamily of numerical methods. However, most of them involve ...
1
vote
0answers
34 views

How can I automatically set an NIntegrate call to zero if NIntegrate::slwcon is observed?

This is a generic question about the NIntegrate function. I am attempting to numerically integrate a function which may or may not be highly oscillatory, based on it's inputs. For a certain sets of ...
0
votes
0answers
63 views

Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
0
votes
0answers
34 views
6
votes
3answers
146 views

Force WhenEvent to respect default stepsize

I have to numerically integrate an equation system and monitor the accumulating datapoints. For example, I fit a line to a subsample of the points and terminate via ...
2
votes
3answers
189 views

What's the proper way to 'cut out' an irrelevant part of an integral, so I don't run into problems with precision?

I'm doing a numerical integration that involves an integrand with a few exponentials whose values over the integration region range enormously. I'm really only interested in the part of the range that ...
6
votes
0answers
209 views

Problems with NDSolve for solving coupled Schrödinger-like PDEs with perfectly matched layer boundary condition

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
0
votes
1answer
74 views

Difficulty using NDSolve

I am tying to solve two differential equations with two delays numerically. The result didn't come out and it was written that “NDSolve::ndsz:...step size is effectively zero; singularity or stiff ...
1
vote
1answer
70 views

NFourierTransform do not show all points, even change PlotPoints and Exclusions

Needs["FourierSeries`"] I try solve the numerical Fourier transform of this function: ...
0
votes
0answers
40 views

NIntegrate a function in a circular segment

I am trying to integrate numerically a function over a circular segment surface using polar coordinates. In the following example I am using the zero order Bessel function, but any cylindrical ...
4
votes
2answers
106 views

Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
0
votes
1answer
61 views

WorkingPrecision and AccuracyGoal for using with NIntegrate

I'm modeling a quantum tunneling barrier. Because I want to express my quantities in mks units, that means that some of the variables I'm using are pretty small (10^-9). I use NIntegrate for part of ...
-1
votes
2answers
117 views

Numerical approximation using trapezoidal formula [closed]

I have bumped into a problem, that I cannot solve. I have to approximate the value of ln3 using a composite trapezoidal formula, so that the error should be within (10)^-3! How can it be solved?
3
votes
1answer
88 views

Trying to find a temperature profile with a nonlinear 2nd order ODE. NDSolve very sensitive to seemingly arbitrary constant

I am trying to solve this differential equation for a heat transfer problem: \begin{equation} kt\frac{\partial^2 T}{\partial x^2} = \epsilon \sigma T^4, \ \ \ T(0) = T_0, \ \ \ \frac{\partial ...
4
votes
1answer
51 views

NIntegrate crashes without error message when using high precision integrand with non-zero tailing digits

I have a numerical integral that evaluates fine for floating point arguments with low precision (e.g., 4 digits), with argument where only zeros follow the first, e.g., 4 non-zero digits, or with ...
6
votes
1answer
103 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
92 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
79 views

NIntegrate discrepancies

I want to compute a numerical integral for a gaussian trivariate distribution. Say ...
5
votes
2answers
94 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
107 views

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

I have the following code in Mathematica. ...
1
vote
2answers
57 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
39 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
55 views

NIntegration and DSolve with same variable

I need to solve this problem: Then follows the code, with: ...
7
votes
2answers
332 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 ...
0
votes
0answers
82 views

NIntegrate non-numerical values error occurs when MaxRecursion is increased

I was doing some numerical integration,and found out when MaxRecursion was low(such as the default 9 times),the integration can have a result with the warning: ...
3
votes
4answers
268 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
107 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
46 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
112 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
54 views

Multiple stopping constraints in NDSolve

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

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
1
vote
1answer
113 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
63 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
votes
3answers
513 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
69 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- ...