Questions on the use of numerical functions NIntegrate and NDSolve.

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6
votes
1answer
543 views

The difference between “SymbolicProcessing” -> 0 and restricting the function definition to numeric values only

The Documentation tells us that there are two ways to disable symbolic processing of the integrand by the NIntegrate function when it is known that it just slows ...
6
votes
1answer
382 views

What does MaxStepFraction do?

I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
3
votes
1answer
1k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
1
vote
0answers
547 views

triple NIntegrate fails

Here's m problem simpler in terms of codes ...
1
vote
1answer
219 views

Syntax for integrating over limits specified by a Table

I wish to use NIntegrate to compute multidimensional integrals. However, I don't want to manually input the limits for the dimensions. I want to store the ...
0
votes
1answer
2k views

Stategies to avoid NIntegrate::slwcon error

I am trying to numerically evaluate an integral whose integrand depends on two parameters, say $(a,b)$ and when $b\gg 1$ I suspect (although it's not guaranteed) that the integrand is very small. Thus ...
7
votes
2answers
249 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns several error messages: ...
7
votes
1answer
403 views
7
votes
4answers
541 views

Conditional numerical integration boundaries

I have a multidimensional integration of the form: ...
3
votes
4answers
208 views
2
votes
1answer
181 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In ...
-3
votes
1answer
107 views

Integration with mathematica? [closed]

I am very new to Mathematica. I am trying to evaluate ∫ (1+lnx)Sqrt(1+(xlnx)^2) using Mathematica. I know a substitution must be done so I have set ...
19
votes
4answers
1k views

How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
13
votes
1answer
498 views

How to guarantee that NDSolve correctly detects abrupt changes in parameters?

When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
14
votes
5answers
329 views

Mismatch between numerical and analytic evaluation of an integral

I evaluated the following integral NIntegrate[Sqrt[r] Abs[Cos[(k + 1/2) Pi r]], {r, 0, 1}] getting as a result 0.413232 for ...
11
votes
3answers
938 views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
5
votes
1answer
300 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 ...
15
votes
2answers
199 views

Least effort to handle a point source inside the domain of PDE(s)

By point source I mean a constrained condition at one point inside the domain of PDE(s). For example: $$\frac{\partial ^2u(t,x,y)}{\partial t^2}=\frac{\partial ^2u(t,x,y)}{\partial ...
7
votes
1answer
415 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
3
votes
1answer
661 views

Monitoring the Evaluation of NDSolve: time to finish estimation

My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the ...
3
votes
2answers
650 views

NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
15
votes
2answers
954 views

Why does Mathematica give the wrong answer when integrating?

I integrate Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}] Mathematica gives: 2 I Pi BesselJ[1, 1] Which is indepedent ...
12
votes
1answer
980 views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
7
votes
2answers
784 views

How to set the NDSolve method to LSODA

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
6
votes
3answers
2k views

How to use results of NDsolve[] for further solving of ODEs?

I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5? An easy example would be $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
5
votes
2answers
149 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
1answer
954 views

Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?

I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs: ...
4
votes
1answer
438 views

Multiple simultaneous events in EventLocator method for NDSolve

I'm using NDSolve to integrate a system of ODEs, and EventLocator to stop the integration when it leaves a certain region in phase space. This works perfectly as it should. However, I've also added ...
1
vote
1answer
144 views

Locating Periodic Orbits

Here is the code for the numerical integration of an orbit. First the module for the definition of the equations of motion. ...
14
votes
1answer
2k views

Parallelizing Numerical Integration in Mathematica

I have an ugly, six dimensional function that I need to integrate numerically. It works, but it currently take twelve hours to complete the calculation. Is there any good way to parallelize the ...
11
votes
1answer
354 views

Boosting the performance of expensive NIntegrate by feeding in a cheap approximation of the integrand

I need to integrate an expensive likelihood L[x] over its n-dimensional domain. I know that L[x] is decently approximated by a ...
9
votes
1answer
175 views

Is this a bug in NIntegrate?

Bug is present as of version 10.0.2 checked on windows 7, 64 bit Is this a bug or I missed something? NIntegrate seems to give a different answer for the same ...
9
votes
1answer
243 views

The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
8
votes
2answers
295 views

Why do I get a different value when I change the order of integration?

I think the following two-dimensional integrals should be equal, since they both integrate the function over the half plane defined by $t>\tau$. $$\int_{-\infty}^\infty \mathrm{d}t ...
8
votes
1answer
973 views

Efficient evaluation of functions defined by NIntegrate

I have a complicated function $f$ and I want to plot the function $F(x)$ defined by the definite integral of $f$ from $0$ to $x$: $$ F(x) = \int_0^x f(y)\mathrm dy. $$ Apparently $f$ cannot be ...
5
votes
1answer
314 views

Proper use of arbitrary number of variables

So, I'm working on a project where the number of independent variables is not fixed. Consider a problem of $N$ independent variables, $\boldsymbol{r}$. I want to perform different things with them. ...
5
votes
2answers
3k 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, ...
4
votes
1answer
202 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
4
votes
0answers
351 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a pieceise function. If we define the ODE system ...
4
votes
2answers
540 views

WhenEvent in NDSolve

How come this doesn't work as I intended? ...
4
votes
3answers
367 views

How could I get the value of y[t] at each specific interpolation point?

sol = NDSolve[{Derivative[2][y][t] + Sin[y[t]] == 0, Derivative[1][y][0] == 0, y[0] == 1}, y, {t, 0, 2}] the above-mentioned differential equations can be solved ...
3
votes
1answer
368 views

Evaluating function only when its optional argument is numeric

I want to have the argument 'a' for myf2 in form of optional argument, but at the same time I need to evaluate the function only if 'a' is Numeric, see also my previous question. ...
2
votes
1answer
233 views

Area between Contours in ContourPlot

I feel slightly foolish for asking this because I am so close, but I'm having trouble, so I will anyway. I asked this question two days ago regarding finding the lengths of contours. Now, I'd like to ...
1
vote
1answer
371 views

NDSolve for PDE with discontinuous initial/terminal condition

I have an issue with NDSolve for the case of a PDE with discontinuous initial/terminal condition. Consider the PDE solution ...
0
votes
1answer
474 views

NIntegrate & non-numerical values

I am wondering why I am receiving the message "The integrand ... has evaluated to non-numerical values for all sampling points in the region ..." for a particular calculation I am running. How can I ...
15
votes
1answer
374 views

Why does LogLinearPlot sample its argument outside the specified domain?

I experience a weird bug in the function LogLinearPlot. If the input is an interpolation function, such as the one created like this, ...
8
votes
1answer
379 views

Setting the DifferenceOrder Option

I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force ...
6
votes
2answers
438 views

Starting NDSolve from intermediate time step?

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from tmin=0 to ...
6
votes
1answer
284 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 ...
5
votes
2answers
542 views

Numerical Integration as Model for Nonlinear Fit

I'm trying to do a fit for parameters of a function within an integral but I'm getting errors when I try and run it. Essentially I want the following fit to work out: ...