Questions on the use of numerical functions NIntegrate and NDSolve.

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4
votes
1answer
98 views

Using `N` gives strange result

Consider these two functions which are almost the same: ...
4
votes
1answer
221 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
401 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
322 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
0answers
293 views

Increase precision of custom function

I hope the title is not misleading: Suppose I have a function that is quite complicated, e.g. f[u_] := Exp[-Exp[- Abs[c.u]^a] Sin[d.u] Sin[(Abs[c.u]^a) ... I ...
3
votes
2answers
209 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
1answer
871 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: ...
3
votes
2answers
527 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
4answers
161 views
3
votes
2answers
328 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
178 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
365 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
398 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
1answer
164 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
314 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
3answers
720 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
1answer
280 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
577 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
700 views

Compute integral symbolically or numerically

I want to compute the integral of the following integrand ...
3
votes
1answer
207 views

Differentiating ParametricNDSolve solutions

Is there any way to differentiate a solution obtained by ParametricNDSolve? For instance, I have the position $\phi_\gamma(t)$ as a function of time, parametrized ...
3
votes
1answer
415 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
69 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
295 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
371 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
554 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
497 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
381 views

Integrating over data points from an external source (wolfram|alpha and weather)

I moved to another city and the weather sucks. Sometimes I feel like getting sad and so I go to wolfram|alpha and check for example ${}$ ...
3
votes
1answer
68 views

NIntegrate on tetrahedron

I've been trying to numerically calculate an integral in a tetrahedron of a discretized domain. In some cases when I specify a method I've been getting the error message NIntegrate::femonly ...
3
votes
2answers
91 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
134 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 ...
3
votes
2answers
397 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: ...
3
votes
1answer
198 views

Integrate equations of motion when force depends on position

I'm fairly new to Mathematica. I'm trying to test my C++ implementation of a fourth order Runge Kutta method for Newton's equations of motion. I want to test my integrator when the applied force is ...
3
votes
1answer
562 views

NDSolve for a large system of simple ODEs

I am solving a system of many (more than 100) ODEs. It is the kind of standard rate equation encountered in semiconductor physics. Here is the system: ...
3
votes
2answers
590 views

NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
3
votes
2answers
394 views

How to set the initial condition? (to make IC and BC consistent)

I want to find the initial condition which fits mixed boundary condition of Phi[r, Theta, t]. The original initial condition in text is Phi[r, Theta, 0] == 1 . ...
3
votes
1answer
172 views

Integrating a functional of an InterpolatingFunction

It is straightforward to Integrate an InterpolatingFunction. However, even for a simple functional of an ...
3
votes
1answer
185 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
296 views

Question on accuracy and precision of NIntegrate

As a Mathematica newbie, I was testing the accuracy/precision of NIntegrate (9.0.1.0 on Mac) and have obtained a very peculiar result. ...
3
votes
1answer
158 views

NDSolve: Reinitialize fails with If condition

I have found a weird problem using If conditions containing an state inequality of the form state<=. First consider the simple ODE with an If condition ...
3
votes
1answer
375 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\ ...
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 ...
3
votes
1answer
326 views

NIntegrate inside NSum

Consider the following function with a numerical integration: ...
3
votes
2answers
111 views

NIntegrate returns zero for non zero integrand, 4d Integration

I am trying to calculate the following integral. ...
3
votes
1answer
198 views

Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
3
votes
1answer
441 views

Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...
3
votes
1answer
401 views

Efficient way to perform elementary integration step with NDSolve internal method

I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via ...
3
votes
1answer
42 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
3
votes
0answers
54 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the follwoing integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, Infinity}, Assumptions -> z \[Element] Reals] >> -3.36354 - 3.85013 I the ...
3
votes
0answers
57 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): ...
3
votes
0answers
49 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 ...