Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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1answer
162 views

Order of evaluation in nested expression

I am trying to make a function that works as follows: Integrate 1 for all t in the interval $ [0,1] $ such that the first element of function vstar is positive. ...
1
vote
1answer
143 views

ParallelTable of ParametricNDSolve objects fail

There seems to be a problem with ParametricNDSolveValue togeteher with ParallelTable First we create a ParametricNDSolveValue object ...
1
vote
1answer
190 views

ParametricNDSolve: Fails to differentiate an matrix differential equation

It seems like there is a problem with differentiating a ParametricNDSolve object when the underlying system contains an matrix differential equation. Create a simple ParametricNDSolveValue object ...
3
votes
1answer
264 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 ...
2
votes
0answers
136 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 ...
16
votes
3answers
777 views

Only final result from NDSolve

Finally, I started to play with differential equations in Mathematica. And I have faced the problem, which seems to me so basic that I'm afraid this question is going to be closed soon. However, ...
1
vote
0answers
149 views

why maxrecursion didn't work if I specify singularity in NIntegrate

I study sigularity specification and MaxRecursion in NIntegrate. And find something unusual. first I define a function δ[x_, y_: 1/100] := 1/π*y/(x^2 + y^2) ...
3
votes
1answer
870 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 ...
10
votes
1answer
360 views

Mathematica9: NDSolve slows down after repeated calls

I have noted that in Mathematica 9 my code, which involves a lot of calls to NDSolve, slows down considerably after some time. Apparently, the problem is NDSolve itself and it seems to be related to ...
5
votes
2answers
506 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 ...
5
votes
2answers
604 views

Volume of a graph

I have the following list: ...
3
votes
1answer
517 views

Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
4
votes
1answer
264 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
590 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
573 views

Crank-Nicolson with NDSolve?

As far as I understand, the Crank-Nicolson method (a.k.a. trapezoidal method) can be expressed as a second order implicit Runge-Kutta method. It's Butcher tableau is: ...
4
votes
1answer
651 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) ...
-2
votes
1answer
722 views

Interpolating Function inside of NDSolve

I have a problem and it seems to be connected to an Interpolating function inside of an NDSolve command. The resistivity[x] ...
0
votes
2answers
895 views

Plot of a function which includes numerical integrals

I want to make a 3D plot of two variable i1 and b1. The dependent variable results from a pay-off function ...
1
vote
1answer
224 views

Using new symbol in WhenEvent in NDSolve

This is an example in Mathematica's help document. ...
10
votes
2answers
408 views

Symbolic integration fails while numerical integration succeeds

I am hoping to evaluate the following integral Integrate[((r^3 - 7)^(2/3)*(1 - (r^3 - 7)^(2/3)/r^2))/r^3, {r, 2, Infinity}] but Mathematica informs me that this ...
8
votes
2answers
387 views

Adding a constant vector to a vector differential equation seems to break NDSolve. Why?

I'm trying to solve a differential equation that's phrased in terms of matrices and vectors. My minimum working example is this: ...
1
vote
1answer
248 views
0
votes
1answer
153 views

Question with ParametricNDSolveValue

When solving the following system: ...
0
votes
1answer
217 views

find derivative with defined function

s[a_, b_] := NDSolve[{y''[x] == y[x] Cos[x + y[x]], y[0] == a, y'[0] == 1}, y, {x,0, b}] I need to find the minimal of $\int _1^by[x]^2$ in the region ...
9
votes
4answers
635 views

NIntegrate extremely piecewised functions

I often need to integrate extremely piecewised functions, like the following one (not extreme, but gives an idea): ...
1
vote
1answer
224 views

Changing ParametricNDSolveValue options for only part of the run

Here is an example of the system that I am running, ...
-2
votes
1answer
353 views

Help in NIntegration Methods - Takes too long, why?

I have this code. It is a triple integral, and using the automatic method gives me a wrong answer for $T=0.1$ (the correct answer is $5.44$, while I got $3.73$ ). I've tried to change the integral ...
-1
votes
2answers
363 views

Performance of numerical optimization with triple integral [closed]

I'm trying to solve a numerical optimisation that looks something like this: ...
5
votes
2answers
774 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
2answers
599 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 ...
8
votes
1answer
617 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
2
votes
0answers
68 views

Are FEM methods integrated in NDSolve yet? [duplicate]

About a year ago there was a discussion on these forums as to whether FEM methods have already been integrated into NDSolve in Mathematica. The answer back then was ...
1
vote
0answers
92 views

Integrate boundaries defined as equations

Have you guys ever needed to define Integrate boundaries as equations? I tried to submit the equation as was written in original text but it seems that mathematica can't understand it. ...
1
vote
0answers
845 views

triple NIntegrate fails

Here's m problem simpler in terms of codes ...
27
votes
2answers
3k views

Complex valued 2+1D PDE Schrödinger equation, numerical method for `NDSolve`?

Based on the heat equation of the Mathematica Manual tutorial, I wrote the complex counterpart (Schrödinger) equation, for the free particle propagation of an initial wavepacket. ...
0
votes
0answers
50 views

Ignoring Indeterminate Results [duplicate]

I am doing some program where I must calculate some numerical integral (the involved function is quite complicated to be solved analytically). The function to be integrated have some parameters which ...
-2
votes
1answer
656 views

Problem with plotting a function with NIntegrate

Why does the following Plot3D command never terminate? ...
6
votes
1answer
427 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 ...
0
votes
2answers
214 views

Is there a better way to approximate some graphs of integrals than interpolation?

I'm still pretty new to Mathematica so my apologies if this is a dumb question. I wanted to plot some integrals of functions for no particularly good reason, but the only decent way I could come up ...
1
vote
0answers
342 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
49
votes
2answers
2k views

When I can assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: ...
5
votes
2answers
322 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
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 ...
1
vote
1answer
254 views

Fast integration of 2D distribution across lines parallel to y-axis

I'm struggling with a small data set and a slow calculation. I have hundreds of small 2D data arrays and need to integrate across several lines parallel to the y-axis. Let me start with the data ...
0
votes
1answer
784 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
4
votes
2answers
1k views

Does Mathematica have a command analogous to ode45 of MATLAB?

Does anybody know if Mathematica has an analogue of MATLAB's ode45 command? I need to solve a second order coupled ODE system of equations.
4
votes
1answer
540 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\ ...
1
vote
1answer
512 views

Simpson's rule with ListConvolve or ListCorrelate

I have a function that's represented as a long list of values that I want to integrate. I can do it procedurally with Simpson's rule. ListConvolve generally runs faster then procedural code, so i ...
12
votes
1answer
367 views

WhenEvent and partial derivatives

Can WhenEvent be used to reset the conditions on a PDE at a given time? How would the syntax of that be? This is the code I`m using ...
1
vote
1answer
384 views

NIntegrate converging too slowly when increasing size of array

I have a problem with a numerical integration. I have a 4x4x4x4 array that has for each entry an integral and I want to use NIntegrate to evaluate it. It gives me ...