Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
3
votes
1answer
99 views
NExpectation not up to expectations with Boole or Conditioned
Context
I am interested in computing numerically the number of extrema at a given threshold for random fields. These numbers are expectations of MultinormalDistributions.
Problem
This integral ...
3
votes
1answer
605 views
How to discretize a nonlinear PDE fast?
I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...
3
votes
1answer
75 views
Find point at which equation stops having roots (if it exists)
I am interested in the roots of this function:
f[M_, b_] := 1 - (2 M Gamma[2, 0, (1/M + b M)/Sqrt[b]])/(1/M + b M)
for fixed values of b. In particular I want ...
3
votes
1answer
177 views
Tutorial for basic numerical methods for PDEs
I'm afraid this is probably not going to be a "good" question, but I'd like to use Mathematica to learn about basic numerical schemes for solving pdes. For example, I'd like to compute the solution of ...
3
votes
1answer
182 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
0answers
115 views
FindRoot gives a wrong solution which obviously should not be there
I got stuck on FindRoot and I didn't see any similar problem posted, so let me explain what I am trying to do and what problem I meet here.
I try to find roots of a particular function, which in the ...
3
votes
0answers
178 views
A is fast, B is fast, but together they're Mathematica-crashing slow?
I'm trying to do something with finding solutions to a quantum mechanics problem with n wells. If there are 40 wells, I need to find the solution to an equation in the form:
...
3
votes
0answers
256 views
How can I solve this complicated custom function numerically?
I have a complicated function that calculates the total value of payments from an account into which deposits are made annually. I'd like to solve the function for a growth rate numerically, but ...
3
votes
0answers
226 views
Numerically solving PDE with high precision
I want to numerically solve the PDE
$\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$
with some initial and boundary conditions and given parameters $c$, $m$ and $l$.
Consider the code
...
3
votes
0answers
122 views
LeastSquare Solution for the Continuous Time Lyapunov Equation
I have been working with a problem which involves solving the continuous time Lyapunov equation
$$A R + R A^\top = G$$
for the symmetric positive definite matrix $R$. Here $A$ is real, invertible ...
3
votes
0answers
160 views
Semidefinite Programming
I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
2
votes
3answers
123 views
How can I name “a[[i]]” the parts of Table “a”? Or how to make Table “a” grow inside FindMinimum?
Let's say I want to minimize a function that uses a Table named a with the Conjugate Gradient Method of ...
2
votes
2answers
283 views
Unexpected result of summation
I wrote small module that gives me 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
2answers
139 views
Position function not always retuning an answer even with no apparent problems
I'm having some problems with Position.
Sometimes it will give an empty list instead of the actual position of the element I am looking for when that element is ...
2
votes
2answers
210 views
Plotting several numerical solutions plus the analytic solution of ODE in one plot
I want to be able to plot several numerical solutions of an ODE plus its analytical solution in one plot in order to see how the numerical solutions converge towards the analytical one w.r.t. the ...
2
votes
3answers
589 views
How can I differentiate Numerically?
Mathematica has two ways to integrate: Integrate and NIntegrate.
But what about D? ...
2
votes
1answer
227 views
How to solve simultaneous equations faster with Compile?
I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
2
votes
2answers
171 views
Weird NDSolve behavior with Piecewise (MMA9)
NDSolve in Mathematica 9.0.0 (MacOS) is behaving strangely with a piecewise right hand side. The following code (a simplified version of my real problem):
...
2
votes
1answer
94 views
Mathematica 7: Problems when evaluating Fourier inside a ParallelTable
after I got such a great response for my first question on this site, I'm very encouraged to asked my second one!
So here it is, very generally: To speed up a "row-wise" (i.e. 1D) operation on a ...
2
votes
1answer
126 views
Numerical comparisons of matrices
I have a matrix which should be equal to a null matrix. However due to the numerical precision, a brutal equality test with a matrix initialized with zeros does not work.
How should I perform the ...
2
votes
1answer
70 views
Numerical Error with Large Matrices
I am writing a Finite Element Analysis program in Mathematica. The code involves handling a large matrix with large entries. I get an error when I try to use Mathematica's "LinearSolve" to solve a ...
2
votes
2answers
86 views
2
votes
1answer
104 views
Computing derivatives of a moment generating function
Dear Mathematica users,
I'm trying to compute higher order derivatives of a moment generating function and then evalutate them in 0 (in order to get some moment conditions for a GMM estimation).
...
2
votes
1answer
155 views
How to solve equations self-consistently
I want to solve the following equation self-consistently. So,
H.u = e.u
{{1, d}, {d, 1}}.{u1, u2} = e.{u1, u2}
I guess an initial value for ...
2
votes
1answer
339 views
intersection between two curves in Mathematica
I have two curves (drawn from points) in a plane, one is drawn with ListLinePlot and the other drawn with ParametricPlot. How ...
2
votes
1answer
251 views
Mathematica NDSolve and 'Compile'?
Since the consensus is usually that NDSolve speeds fares badly against compiled code such as c++ ODE solvers using GSL say, is it possible to make up for this lag ...
2
votes
0answers
51 views
Speeding up a numerical constrained quadratic optimization
I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$:
$$
\begin{aligned}
&\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
2
votes
0answers
31 views
NIntegrate/NSum with parameters [duplicate]
I'm trying to calculate a continuous integral within a discrete integral.
Something similar to this (yet more complex):
...
2
votes
0answers
137 views
Minimization in mathematica [closed]
I have recently had a strange problem with NMinimize. I have a very huge function with respect to 20 parameters. When I ...
2
votes
0answers
173 views
Numerically/Analytically Solving a System of Equations
I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
2
votes
0answers
115 views
Why to do parentheses change the results of a calculation?
I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2
...
1
vote
1answer
167 views
Why is arithmetic faster for inexact arithmetic?
I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...
1
vote
1answer
93 views
why there is a small imaginary part [closed]
I encountered a problem. I have a eigenvector eigvsI[1]
...
1
vote
1answer
220 views
1
vote
2answers
180 views
Quickly differentiate and evaluate a function of several variables
How can I differentiate a function with respect to several variables and evaluate it at the same time ? I want to specify also the variable index that I want to differentiate and the number of times I ...
1
vote
2answers
280 views
Running a Numerical Simulation on a System of Differential Equations with unique initial conditions
I have a system of differential equations as follows:
...
1
vote
1answer
345 views
Forcing FindRoot to return only real solutions
FindRoot documentation reports that if the Equation and the initial point are reals, the solutions are searched in the real domain.
However, in the following case I ...
1
vote
2answers
125 views
How can I use FindRoot on an expression from NDSolve?
I have a second order ODE that I can only solve numerically using NDSolve, but I then need to use the solution in FindRoot and am running into errors. A simplified but analogous problem is the ...
1
vote
1answer
170 views
1
vote
1answer
108 views
Why does NSum fail here?
I want to evaluate a sum of integrals; each integral has a pole on the real axis and I handle this via the Cauchy Principal Value
$ ...
1
vote
1answer
107 views
Seemingly simple optimization problem is slow
I'm trying to generate a demand curve numerically, given a utility function. The function for the demand is defined like so:
...
1
vote
2answers
81 views
NSum generates a warning message when getting the sum of a list
I know what I'm doing can be done with Total:
a = Range@3;
Total@a
And if I simply choose ...
1
vote
3answers
282 views
equation solving problems
I have some equation:
$$
veq=-2-lr-l^2r+2(r+ir^3\omega) v' + (-2+r)r^2v'^2 + (-2+r) r^2 v''==0
$$
or in Mathematica form:
...
1
vote
1answer
64 views
Plot FindRoot for non-trivial function
I would like to plot the results of FindRoot over certain range of inputs. I tried to do this with the code:
...
1
vote
1answer
48 views
Can't see updating performed by NMinimize[…,StepMonitor->(…)] outside of Button in which it's called [duplicate]
I've made a peak-fitting GUI in which I have a "Fit" button that, when pressed, calls NMinimize[...,StepMonitor->(step++)] to minimize a sum of squared ...
1
vote
1answer
118 views
How can I handle curve singularity in this NIntegrate integration?
Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region.
(Why ...
1
vote
1answer
104 views
How to calculate an integral of an expression that is determined numerically (in Mathematica)?
First of all, I am fairly new to Mathematica and Stackoverflow, so please feel free to give me any advice whatsoever.
I aim to calculate an integral of an expression that has been determined ...
1
vote
1answer
173 views
Why is NDSolve solving in term of two 1st order ODE slower than 2nd order?
As mentioned in the documentation for NDSolve it's often convenient to reduce a 2nd order ODE to a system of first order equations. When I do this however I seem to see a significant speed reduction ...
1
vote
1answer
286 views
NDSolve runs out of memory
I need to solve a second order ODE numerically. The ODE depends on two parameters (a,b). Things work fine when 'a' is small, but for large 'a' the solutions are oscillating rapidly and Mathematica ...
1
vote
1answer
491 views
Problem while solving system of two second order non linear coupled differential equations using NDSolve function
I am a completely new to Mathematica, and I am sorry if this question is dumb. I have to solve a system of two second order non linear coupled differential equations (that I got from the Lagrangian ...
