Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

6
votes
1answer
312 views

Strange Behaviour of NIntegrate

I found some of the values remained unevaluated using the following code Table[NIntegrate[Sin[i x]/((2^x + 1) (Sin[x])), {x, -Pi/2, Pi/2}], {i,70, 90}] Pick them ...
6
votes
2answers
248 views

When analytical and numerical methods do not agree - Case study with Maximum Likelihoods methods

Here is the probability distribution I am interested in: $$P(q)=C e^{4 n s q} q^{4 n \nu - 1} (1 - q)^{4 n \mu - 1}$$ , where $e$ is the constant of Euler and $C$ is constant so that the whole thing ...
6
votes
2answers
212 views

Why does Nintegrate keep unevaluated?

Bug introduced in 10.0 and fixed in 10.2.0 It's no surprise that the "MonteCarlo" Method works well: ...
6
votes
2answers
217 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...
6
votes
1answer
934 views

WhenEvent in NDSolve

How come this doesn't work as I intended? ...
6
votes
2answers
334 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
6
votes
1answer
105 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 ...
6
votes
1answer
804 views

NestList and Euler's method

I am new to mathematica and so just experimenting with various programming constructs. Recently have been looking at NestList and how I could use this to implement ...
6
votes
1answer
296 views

Getting Integrate to perform numerical integration

I am trying to calculate the mutual impedance of two antennas which is just a big integral. I defined my function in terms of my variable, but when I execute it, Mathematica runs for a while and then ...
6
votes
1answer
774 views

Unexpected results from NDSolve

I am trying to solve a stiff reaction diffusion system with NDSolve. However, it does not produce the expected results. My problem is a spherical cell with 5 ...
6
votes
1answer
538 views

What does MaxStepFraction do?

I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
6
votes
1answer
491 views

Specifying mesh in NDSolve

I am trying to solve a system of one-dimensional two-point boundary-value problems with NDSolve. I would like use a fixed mesh (specified by me) in the calculation. Is there a way to do this? The ...
6
votes
1answer
107 views

Spurious infinite limit of integration message in NIntegrate

Bug introduced in 7.0 and persisting through 10.2 NIntegrate returns an error complaining that ComplexInfinity is an invalid ...
6
votes
2answers
5k views

How to handle NDSolve::ndsz problem (singularity problem)

I have 2 second order differential equations (non-linear). The physics behind them is correct. I verified the equations many times. It is a solid pendulum with a mass-spring at the end of it. Now, ...
6
votes
1answer
141 views

What boundary is added when NDSolve::bcart pops up?

When insufficient boundary conditions are given to NDSolve for solving PDE, the warning NDSolve::bcart pops up: ...
6
votes
2answers
582 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a piecewise function. If we define the ODE system ...
6
votes
1answer
695 views

Preconditioning the objective function of NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
6
votes
0answers
239 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 ...
6
votes
0answers
130 views

Slow NIntegrate over complicated domains (sometimes)

This is no longer a problem with Mathematica 10.* where I can use regions to do the integrations Overview I have a very large matrix I need to calculate where each element requires the integration ...
5
votes
1answer
1k views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
5
votes
2answers
2k views

How to plot and solve the numerical solution of a integro-differential equation

I have a integro-differential equation of the form $y'(t) = - \int_0^t {y(t_1 )} e^{t_1 - t} dt_1, {\rm{ t}} \in {\rm{[0,10], y(0) = 1}}$ My code is: ...
5
votes
2answers
609 views

Volume of a graph

I have the following list: ...
5
votes
3answers
208 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: ...
5
votes
3answers
137 views

Differentiate a numerically defined function

My function is f[a_, b_] := NIntegrate[Sqrt[(Cos[t] - a)^2 + b^2], {t, 0, Pi}] I want to calculate g[1,1] where ...
5
votes
5answers
1k views

NIntegrate::slwcon Problem

I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate[] needs a lot of time to calculate this. Is there any way to ...
5
votes
3answers
1k views

How to deal with zero in NDSolve in mathematica?

I would like to solve the following ODEs $$\begin{cases} x'(t)&=y\\ y'(t)&=-y(t)/t-e^{x(t)},\\ x(0)&=1,\\y(0)&=0, \end{cases}$$ (EDIT : The second equation used to be $y'(t) = -x(t)/...
5
votes
4answers
253 views

error with NIntegrate and RegionPlot

Bug introduced in 10.2 or earlier and persisting through 10.2 or later Here's a simplified example of what I'm trying to do: ...
5
votes
1answer
2k views

NDSolve, Schrödinger equation, and decaying solution

I am trying to solve a Schrödinger equation for a particle hitting a step potential using NDSolve in Mathematica. Here is my code: ...
5
votes
2answers
99 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 ...
5
votes
2answers
898 views

Animating the Lorenz Equations

I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck. The equations are: $\begin{...
5
votes
1answer
365 views

NDSolve and WhenEvent Causing Excess Work

When I use the following system model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5} with the ...
5
votes
2answers
173 views

How to speed up Integration of interpolation function?

I have a list of data, and I interpolate it to a function. Then I need to do an integration with the interpolating function. But I found that the speed is unacceptably slow. My data is here (a little ...
5
votes
2answers
292 views

FEM giving “ … is not a polynomial error”

Executing the program below I get the ... is not a polynomial error message. I don't have an idea why I am getting this -- any suggestions? ...
5
votes
2answers
154 views

Example of Integrate applying a numerical evaluation N

Here is a minimal example: Integrate[(a[1] + x)^2, {x, 1., 2.}] 2.33333 + 3. a[1.] + 1. a[1.]^2 The problem is that ...
5
votes
2answers
470 views

How to find Matano plane

I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
5
votes
1answer
188 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 ...
5
votes
1answer
365 views

Why does DSolve give a different result than NDSolve?

When I try DSolve to solve a system: ...
5
votes
2answers
184 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
5
votes
1answer
408 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
5
votes
1answer
149 views

memory leaks using NIntegrate on parallel kernel

Bug fixed in version 10.2.0 I'm running a large computation in parallel and the memory usage of the parallel kernels is increasing with every iteration of the calculation. Neither ...
5
votes
1answer
213 views

Slow exponential evaluation over lists

This question,which is still unanswered, might be relevant because it involves NIntegrate over lists and it also has Exp. In ...
5
votes
1answer
303 views

Integration of Two Manipulatable Cylinders

Introduction I created the following code to simulate the many possible interactions between a cylindrical protein crystal and a x-ray beam during serial femtosecond crystallography. ...
5
votes
1answer
705 views

How to improve the solution of a double pendulum system

First, the code: ...
5
votes
2answers
290 views

Integrating a list of functions

For the purpose of this minimal example, let's say we have a list of functions, like this: f[y_?NumericQ] := {NIntegrate[z*y, {z, 0, 1}], a y} I want to ...
5
votes
1answer
95 views

In a PDE solution let us integrate out one of two coordinates

Here is a trapezoid within which I am solving a simple Laplace equation with the Dirichlet boundary conditions set at its top and bottom: ...
5
votes
1answer
411 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 ...
5
votes
1answer
144 views

Integrate over implicit 1D region: works for algebraic but not transcendental equation?

QUESTION How come this works: NIntegrate[1, {x, y} ∈ ImplicitRegion[{x == y^3, x <= 1, x >= 0}, {x, y}]] But this fails: ...
5
votes
2answers
177 views

How to add (energy) constraint when using NDSolve to Equation of Motion

To simplify my problem, I will try and solve the Equation of Motion for a particle in a 1D Harmonic Potential. energy[x_, p_, m_, ω_] := p^2/(2 m) + (m ω^2)/2 x^2 ...
5
votes
1answer
256 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; \...
5
votes
2answers
2k views

Calculating the area under a curve, but above a certain threshold value

so here I am with a time series of data (hours (t) and corresponding measurements (a)). ...