Questions on the use of numerical functions NIntegrate and NDSolve.

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8
votes
1answer
1k 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 ...
7
votes
1answer
93 views

Unify the sampling of NIntegrate[ {f, g, h} w ]

I'm trying to numerically integrate a function which has a vector-valued slow part and a much faster component which is shared by all the components, i.e. an integral of the form $$ ...
5
votes
1answer
236 views

What's wrong with NIntegrate with “MonteCarlo” Method?

My code is: NIntegrate[1, x \[Element] ImplicitRegion[(x > 5 && x < 9) || (x > 11 && x < 13), {x}], Method -> "MonteCarlo"] ...
5
votes
1answer
203 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
1answer
365 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
224 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
400 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
658 views

WhenEvent in NDSolve

How come this doesn't work as I intended? ...
3
votes
1answer
266 views

Numerical integration's speed

Consider this numerical integration of Bessel function: Do[NIntegrate[BesselJ[2, x], {x, 0, 10000}], {i, 1, 100}] // AbsoluteTiming {4.033403, Null} This is ...
3
votes
1answer
460 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. ...
3
votes
2answers
467 views

BC for transport equation using NDSolve

First I can solve a transport equation with a source (Is it still called transport equation?) using DSolve. The form of the source serves only as an example. It can ...
3
votes
2answers
564 views

Unexpected result of summation

I wrote a small module that gives me an incorrect output-set. It should be a single number! I don't understand what went wrong. This is the form of summation used: $$\frac{1}{2} (b-a) \sum_{i=1}^n ...
2
votes
1answer
58 views

Why isn't Table iterator value inserted in failed NIntegrate arguments?

Consider this simplest example: Table[{z, NIntegrate[f[x], {x, 0, z}]}, {z, {1}}] Here f is not defined, so ...
2
votes
1answer
283 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
186 views

NDSolve with arrays and Tables of Equations and WhenEvent

I've been toying around with NDSolve for a while, and read through the website. By doing so I discovered that I could use it for vectors and arrays with much pleasure. So I wanted to write a simple ...
1
vote
1answer
435 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
606 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
394 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
416 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 ...
7
votes
2answers
260 views

How to solve the differential equation with Duhamel's integral?

How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve, but failed: ...
6
votes
1answer
287 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
1answer
140 views

Why does Nintegrate keep unevaluated?

It's no surprise that the "MonteCarlo" Method works well: ...
5
votes
1answer
955 views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
5
votes
2answers
627 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: ...
3
votes
1answer
113 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: ...
3
votes
1answer
95 views

NIntegrate and Interval regions

NIntegrate does not seem to like Intervals as regions. Consider the following example function defined for a parameter "a" ...
3
votes
2answers
214 views

NIntegrate giving message NIntegrate::slwcon:

I got this interesting answer from Mathematica when trying to integrate my function numerically: f[x_] := Sqrt[17*x^2 + x^4] NIntegrate[f[x], {x, -1, 2}] ...
3
votes
1answer
245 views

Surface area of intersecting spheres

Given a sphere of radius 1 centered at the origin and $n$ spheres with radii $r_i$ centered at predefined coordinates, $c_i$, in space, I am after the surface area of the unit sphere that is not ...
3
votes
1answer
226 views

Convergence in NIntegrate vs Integrate

I am faced with this situation that for a certain integration, $\int _0 ^\infty \frac { \tanh (\pi \sqrt{x} )} {\sqrt{x+10} } dx$ - the command Integrate returns ...
3
votes
1answer
536 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) \dot{a}_{\ell} ...
3
votes
2answers
465 views

Speed of convergence for NIntegrate

I'm trying to optimise numerically a function that entails computing the expected value of a truncated trivariate normal distribution and this is taking extremely long -I also get warned about ...
3
votes
1answer
550 views

How to adjust parameters to experimental data on a NDSolve problem

I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3. ...
3
votes
1answer
342 views

Could the PrecisionGoal for NDSolve be a negative number?

The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
3
votes
1answer
492 views

Solving an ODE numerically

I really appreciate it if anyone helps me with this: How can I solve this ODE and plot the answer for $x$ on $[0.6,5]$: $$ \begin{align*} -2xy'[x] = y''[x]+ 47.21 (-.0025 x^6 & + ...
2
votes
1answer
195 views

(NDSolve) Non-linear 2nd order ODE, regular singular point (looking for good methods for this problem)

I am solving this set of non-linear 2nd order ODE by NDSolve, $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ $$\frac{d}{dr}\left[r^2\frac{dh}{dr} \right]=2h(1-f)^2+\lambda ...
2
votes
1answer
75 views

WhenEvent error in NDSolve

I’m trying to solve a discontinuous differential equation where there are lost of energy when the trajectory cross the discontinuous manifold. The code I used was ...
2
votes
2answers
204 views

Plot result of non analytical-integral

I have the following function: h = 1; c = 1; k = 1; B2 = (2*h*c^2)/(x^5 (Exp[(h*c)/(x*k*T)] - 1)); (someone can see that this integral is the Planck function). ...
2
votes
1answer
54 views

Double application of NIntegrate produces unexpected error messages [duplicate]

In the course of trying to answer 69601, I encountered unexpected error messages. In highly simplified form, NIntegrate[NIntegrate[z y, {y, 0, 10}], {z, 0, 10}] ...
2
votes
1answer
120 views

How to use slots and patterns to reduce repetitive calculation?

This is kind of complicated... How can we make MMa calculate values of a function before doing multiple pattern or slot substitutions? Answers to similar questions didn't cover the case where the ...
2
votes
2answers
111 views

FindFit working with Integrate but not NIntegrate - I am using “?NumericQ”

I'm having some syntax problems with finding a fit to an equation that doesn't have an analytical expression for it's integral. Because I think the problem is one of syntax, I am substituting a ...
2
votes
1answer
175 views

Catastrophic loss of precision

while I am trying to solve the double integral in the range of 0 to Infinity (for both the integral) it give me the error Catastrophic loss of precision in the global error estimate due to ...
2
votes
2answers
354 views

What is the proper way to operate on interpolating functions?

I am trying to multiply an interpolating function by -1. If I do this Mathematica does not seem to allow any further operations. Bear with me while I generate the Interpolating Function in question. ...
2
votes
0answers
72 views

Nested NIntegrate of vector function

I am performing a nested integration where the upper limit of the inner integral depends on the value of the outer integral, like in the question [Nested NIntegrate]. As in this question my function ...
2
votes
2answers
219 views

NIntegrate piecewise vector function

Is there a way to numerically integrate a vector function defined via Piecewise? Example: ...
2
votes
1answer
528 views

Use Euler method to solve differential equation

Use Euler's Method or the Modified Euler's to solve the differential equation ${dy/dt=y^2+t^2-1, y(-2)=-2}$ on $[- 2, 2]$. Take h = 0.2 (...
2
votes
0answers
117 views

Whether NIntegrate evaluation is multithreaded or not?

About MultiThread evaluation I am talking about here, see this post I am NIntegrate the function grarm[e, 3, dimension, 1, 1, 0.005]. There is matrix operation in ...
2
votes
1answer
316 views

Using NDSolve solution as initial condition for another NDSolve

I have solved a PDE numerically using NDSolve, and I now need to be able to use that solution as an initial condition for another ...
2
votes
1answer
626 views

Problem with NIntegrate in NonlinearModelFit

We are receiving many error messages when using NIntegrate with NonlinearModelFit. Here is a much-simplified version of the code. It arrives at the correct answer after several messages saying that it ...
2
votes
1answer
684 views

Differential equations with jump conditions

Suppose I want to solve an ODE with a DiracDelta source term. In the following example, DSolve does it correctly while ...