Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

4
votes
1answer
192 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be ...
4
votes
1answer
114 views

Possible bug / numerical issues with HypergeometricU — any suggestions for a fast workaround?

I've encountered some problematic behaviour with HypergeometricU. I have a probability distribution on the positive integers that takes the following form after ...
4
votes
2answers
856 views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
4
votes
1answer
233 views

How to demonstrate lack of stability with advection equation

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good ...
4
votes
1answer
497 views

Multi-dimensional integral in the complex plane with poles and essential singularity

I've passed the last week searching a way to numerically integrate this multi-dimensional integral in the complex plane at the poles and avoiding the singularity at z=0: $$ \oint_{C}\oint_{C\ auound\ ...
4
votes
1answer
363 views

Error Interpretation in NIntegrate

I am using a recursion algorithm developed by Migdal for Lattice Field Theory, and I have the following code: ...
4
votes
2answers
863 views

How to Solve this ODE with Mixed Boundary condition

I have an ODE equation which is sort of y''[x] + 2 y'[x]/x + .0001 (y[x])^3 ==0 subject to the boundary conditions ...
4
votes
1answer
581 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
4
votes
2answers
2k views

PDE Boundary Conditions

I am solving a PDE using Mathematica and I would like to know how to implement the condition that the two-variable function y[t,s] is zero whenever ...
4
votes
1answer
119 views

Using `N` gives strange result

Consider these two functions which are almost the same: ...
4
votes
1answer
297 views

How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
4
votes
1answer
528 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 ...
4
votes
0answers
59 views

Using indexed array elements as integration dummy variables with EvaluationMonitor. Bug?

As part of a routine that must cope with integration of varying numbers of dimensions, I would like to use indexed variable names (e.g., x[0], x[1],...) as dummy integration variables. However, it ...
4
votes
0answers
64 views

NIntegrate::ncvbr: How should we interpret and handle this error not mentioned in any documentation?

I have some user-defined module describing my integrand which has to be computed numerically (it's much more complicated than this but bear with me): ...
4
votes
0answers
75 views

What are good/best practices to take the Fourier transform of an InterpolatingFunction?

I have a function which I have obtained from numerical integration of a differential equation, and I would like to take its Fourier transform. What are good practices for doing this? To make things ...
3
votes
2answers
611 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 ...
3
votes
3answers
165 views

Inefficient NIntegrate and Which

In version 10 a simple numerical integraton of piecewise function is highly inefficient: ...
3
votes
2answers
356 views

How to numerically integrate this integral

I am unable to do this definite integral in Mathematica 9. Is there any command so that I can get the numerical value of the above integration? Code: ...
3
votes
1answer
2k views

Methods to speed up numerical NDSolve, NIntegrate,

I am not very used to do numerical simulations on Mathematica. Do you have any ideas how to improve i.e. speed up my code? ...
3
votes
2answers
261 views

Integration and Fourier transform

I would like to calculate the distribution function from the characteristic function. There is a formula given as $$F_X(x)=\frac{1}{2}+\frac{1}{2\pi}\int_{0}^\infty \frac{e^{i w x}\phi(-w)-e^{-i w ...
3
votes
2answers
705 views

How to avoid this kind of numerical error caused by extreme parameters when using NDSolve?

Here I use a one-dimensional heat conduction equation as the example. I found that when the thermal diffusion coefficient is small enough, Mathematica will give a result against the second law of ...
3
votes
3answers
209 views
3
votes
2answers
152 views

Integrate and NIntegrate not the same

Why am I getting two different results here? ...
3
votes
4answers
289 views
3
votes
2answers
120 views

Help with Integration

I am new to Mathematica, and I need help with integration of the following Reliability expression (from a well-known Reliability Model). $$R(t)=e^{-Ne^{-bt_i}(1-e^{-bt})}, t \geq 0$$ I have ...
3
votes
2answers
516 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
3answers
1k views

How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
3
votes
2answers
485 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
79 views

Maximizing a function defined using NIntegrate [duplicate]

I have two functions fn[x,y,z] which is in integral form and I have another function gn[x,y] which is also in integral form ...
3
votes
2answers
103 views

How should I tweak the options in NIntegrate?

I'm trying to obtain an accurate result from a difficult-to-integrate function and I've thrown in the kitchen sink worth of options in NIntegrate. I think I'm ...
3
votes
1answer
219 views

What method does `NIntegrate` uses by default?

There is a variety of algorithm for performing numerical integration (See wiki). What method does NIntegrate uses by default? I looked on the documentation page and I saw that the function ...
3
votes
1answer
246 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
664 views

Why this numerical integration takes so long?

Let me explain the problem. I am trying to integrate a one dimensional integral: $$\int {g\left( {{k_x}},parameter1,parameter2,...\right)d{\mkern 1mu} {k_x}} $$ for the sake of clarity, I will give ...
3
votes
1answer
489 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
1answer
490 views

Solving the Sine Gordon PDE in mathematica

how can i solve this equation in mathematica? this is sine-gordon eq. but the boundary condition can not recognized by mathematica . thank you for you attention. ...
3
votes
3answers
3k views

Retrieve values of InterpolatingFunction

While analyzing a large system of ODE's, I defined a particular ratio p, which contains some variables that are represented by ...
3
votes
2answers
1k views

Area or NIntegrate curves defined by points?

Is there a convenient method to compute the AUC (Area Under the Curve) metric that quantifies a Receiver Operating Characteristic (ROC) like shown here? The data used to build the ROC are just ...
3
votes
1answer
362 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
652 views

NDSolve Problem

I am trying to solve a chemical equilibrium ODE with NDSolve where one function is the argument to another. I.E. My equations look like: ...
3
votes
2answers
840 views

Compute integral symbolically or numerically

I want to compute the integral of the following integrand ...
3
votes
2answers
997 views

Problem with setting working precision in NIntegrate

I want to obtain a good numerical approximation (up to 10 decimal place would be ok for me) to an integral: $$ \int^{\infty}_{0} f(r)r^2dr $$ I am using the function $f(r)$, which is related to the ...
3
votes
1answer
699 views

Singular integral: NIntegrate fails to converge

I need to calculate the following singular integral: NIntegrate[Log[1 + y^2]/Cos[Pi y], {y, 0, 1}] However, it is failing to converge. I have tried to specify ...
3
votes
1answer
498 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 & + ...
3
votes
1answer
114 views

Precision of NIntegrate

At the moment I am considering a "difficult", highly-oscillatory integral in Mathematica. It calculates the integral without any complaints. However, I am also trying out a numerical method with which ...
3
votes
1answer
121 views

How to evaluate differential entropy from raw data?

I want to evaluate the differential entropy according to here $$h(X) = - \int f(x) \log{f(x)} dx$$ where $f$ is the probability density function. Lets create some test data (normal distribution): ...
3
votes
1answer
126 views

Calculate the relationship between the duration of two oscillating functions

I am trying to quantitatively determine the relationship between the length of two oscillating functions. Meaning, what is the duration of the green spike in relation to the blue square? Does anyone ...
3
votes
1answer
375 views

A Bessel & Struve functions related integral

I try to numerically compute this integral and I don't figure out why on earth Mathematica is not able to do it. Is my input correct? Does it possibly have a closed form? ...
3
votes
1answer
564 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
1answer
866 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
1answer
594 views

NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...