Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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3
votes
0answers
331 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
1answer
455 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: ...
17
votes
1answer
976 views

Optimizing a Numerical Laplace Equation Solver

Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
2
votes
1answer
605 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: ...
3
votes
1answer
108 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 ...
1
vote
2answers
406 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
161 views

FindMaximum inconsistency

The code below seems to work for n<11. But for n=11, and above, it outputs newa then just outputs "beep" sound. WhyTheBeep says "The kernel Local has quit ...
1
vote
1answer
283 views

How to guess initial complex value for FindRoot

I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
2
votes
1answer
428 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
189 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 ...
0
votes
1answer
775 views

Minimization problem using FindMinimum. Functional value “is not a real number”? [closed]

This question is a follow-up of another one I asked a few days ago. I followed the instructions given in the answer provided by the user that responded. I modified that answer to solve another ...
3
votes
2answers
230 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
12
votes
2answers
637 views

Numerical partial derivative

For a one-variable numerical function, it's simple to calculate the derivative at a point with Derivative as Szabolcs has pointed out before: ...
3
votes
1answer
184 views

Strange behaviour of PolyLog Function

I discovered some strange behaviour of the PolyLog[] Function in Mathematica which seems to me like a bug in the function implementation. It looks like ...
0
votes
1answer
272 views

What is the correct way to use NIntegrate inside the FindMinimum function?

I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
4
votes
4answers
244 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 ...
15
votes
4answers
402 views

How to remove duplicates from set of machine precision 2D points?

I have a set of 2D points with machine precision coordinates. I need to remove all duplicates. Performance is important. This is the most obvious fast solution: ...
1
vote
1answer
197 views

What do these error messages mean when numerically solving differential equations?

I am using Mathematica to numercially solve the following equations: ...
3
votes
1answer
920 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 ...
0
votes
1answer
156 views

Alleviating a bottleneck involving a function call with symbolic derivatives

I have a bottleneck problem involving a function call with symbolic derivatives. I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
2
votes
1answer
189 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 ...
6
votes
0answers
136 views

Mathematica 7: “LessEqual::nord:” error when using NMinimize on a real function

I encounter a problem (Mathematica 7) similar to Strategies to avoid LessEqual::nord in NMinimize? but the advised strategies don't work for me. Also, I get different results with different ...
1
vote
1answer
104 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
2answers
530 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
0answers
137 views

Why is FindRoot initial value far from the specified one?

I am trying to numerically find the root of a function that looks a bit like: 1/x - (SchurDecomposition[A[x]][[2]])[[1]], where ...
1
vote
2answers
456 views
15
votes
1answer
1k views

2D Heat equation: inconsistent boundary and initial conditions

I'm attempting to use NDSolve on a 2D boundary value problem with initial conditions. Upon running my code, I get the following message: "NDSolve::ibcinc: Warning: Boundary and initial conditions are ...
3
votes
0answers
318 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: ...
8
votes
4answers
704 views

Numerical integration of a numeric data available as a nested list

I have some numerical data in the form of a list with the following structure: {...{x,y,z},...} defining a surface z=z(x,y) in a 3D space (x,y,z). The data came from a simulation, and I am ...
0
votes
1answer
189 views

How could we define a function recursively?

Let us first consider the constructon of the following simple iteration ...
2
votes
1answer
692 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 ...
1
vote
1answer
220 views
4
votes
2answers
376 views

Finding all/most roots of a discontinuous function more consistently?

I have the equation: f[x_]:=α Tan[α*a] - Sqrt[c - α^2] and ideally I want to find all of its positive zeros, given a and c, with variable alpha. The problem is ...
-2
votes
1answer
191 views

Problem with solving a differential equation [closed]

I need to solve the following differential equation: NDSolve[{R[r, t], R[r, 0] == r/1000}, R, {t, 0, 30}, {r, 1, 30}] Where ...
2
votes
1answer
495 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
272 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
459 views
1
vote
1answer
223 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 ...
2
votes
1answer
2k 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 ...
0
votes
0answers
160 views

Rounding values [duplicate]

In Mathematica 8 when I enter 1 - 0.99 - 0.01 I get 8.67362*10^-18 instead of zero. How do I fix this problem? I am getting ...
0
votes
1answer
369 views

Boundary Value Problem

I have to solve this boundary value problem: $$\frac{\mathrm{d}e_{3x}}{\mathrm{d}l}=(M_0+F_{0z}x-F_{0x}z)e_{3z}$$ $$\frac{\mathrm{d}e_{3z}}{\mathrm{d}l}=-(M_0+F_{0z}x-F_{0x}z)e_{3x}$$ ...
1
vote
1answer
142 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: ...
2
votes
1answer
175 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). ...
8
votes
2answers
360 views

Precision differences

I run this sum and get the symbolic answer below : Sum[ (1/(k^2 - k) - 1/k^2), {k, 2, Infinity}] $2 - \frac{\pi^2}{6}$ I look up the sequence on OEIS and ...
13
votes
3answers
342 views

Make mathematica treat $e_i^2$ as numeric

With NumericQ[symbol] = True, I can declare that a symbol is numeric. I want the expressions matching: $$e_{\text{i$\_$}?\text{IntegerQ}}^2$$ to be treated as ...
5
votes
1answer
224 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
0
votes
1answer
111 views

Non solutions returned by NSolve. And why does it return both phi and Cos[phi]?

Similarly to this thread NSolve gives additional solutions that don't satisfy the equations! NSolve returns "spurious" solutions, even increasing the working precision ...
4
votes
1answer
205 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
1
vote
1answer
201 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 $ ...
2
votes
0answers
329 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, ...