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

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0
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1answer
36 views

Can't sort my list numerically for larger numbers than 10 e.g. 1,10,100,2

I want my files names in real numerical order so 1,2,3,10,12. However it is currently putting them in order like so: 1,10,12,2,3 Input: ...
-1
votes
0answers
33 views

Boundary Conditions that depend on each other [on hold]

I have to numerically solve some 4th order differential equations: B''''(r)=f(r,B,B',B'',B''',S,S'), S''(r)=g(r,B,B',S,S') I'm trying to use the shooting method ...
3
votes
0answers
63 views

Low accuracy while solving a multi-variable equation numerically

My question is as following: I was trying to make a function Vs2[r] with two parameters fit a set of conditions. Vs2[r]: ...
1
vote
1answer
70 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by ...
3
votes
1answer
62 views

Split Boundary Value Problems win Algebraic Equations

Is it possible at all to solve with NDSolve (or other built in function) a split boundary value problem with algebraic equations? Please look at the following example: ...
3
votes
2answers
240 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
6
votes
3answers
244 views

Labeling solutions of an Eigenvalue equation involving Bessel functions

I'm solving the Schrödinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation: $$J_m(k\,R_1)\,Y_m(k\,R_2) - ...
13
votes
1answer
198 views

Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square

I have recently been plotting eigenfunctions of the laplacian over the unit square using the NDEigensystem command. However, I have noticed something in the plots ...
4
votes
6answers
874 views

Randomly Multiply OR Divide by a Random Number?

I want that Mathematica decides randomly if a given variable, gets multiplied or divided by a random number in a given range. The "naive" idea to just use ...
0
votes
0answers
73 views

Errro in plotting the results of FindRoot [closed]

I would like to plot the results of FindRoot over certain range of one input. First of all I am sorry that the equation is a bit long and messy. I have tried to ...
2
votes
1answer
86 views

Basic 2D convolution with mathematica

Can anyone tell me why the following keeps burning my CPU without ever producing the desired plot? ...
3
votes
0answers
74 views
22
votes
3answers
764 views

Exponential fitting - isn't actually a BUG there?

There are many questions on this site about wrong exponential fitting in Mathematica but no one considers this well-known problem as a potential bug. Usually people suggest well-known workarounds ...
1
vote
0answers
74 views

Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ [closed]

I have been following the method for numerically solving the Helmholtz equation in this example (the answer by User21) and have come across two problems. I have been implementing the method for a 2x1 ...
2
votes
3answers
72 views

Smooth initial data

I need something that produce pseudorandom smooth initial data for modelling phase separation equations (Cahn-Hilliard and simular). Generator code for now: ...
4
votes
1answer
53 views

Computing the logarithmic spectral norm rapidly

I wish to compute the logarithmic spectral norm of a square matrix $A$, which is defined by \begin{equation} \mu_2[A]=\lim_{t\downarrow0}\frac{\|I+tA\|_2-1}{t}. \end{equation} Hence, I simply code ...
0
votes
0answers
29 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
0
votes
0answers
62 views
0
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1answer
90 views
5
votes
1answer
170 views

Trouble with shooting method for a 4th-order stiff ODE

The ODE I need to solve is $$\left(y^3y^{\prime\prime\prime}\right)^\prime+\frac{5}{8}xy^\prime-\frac{1}{2}y+\frac{c}{y}=0$$ where $\prime$ denotes differentiation, $c$ is a constant and ...
1
vote
1answer
51 views

Paramter Scans and $\chi^2$ Test in Mathematica

Is there any in-built function or a recommended package that enables one to find, say, 10 Parameters, which are used as boundary conditions in NDSolve, that minimize $\chi^2$? ...
1
vote
1answer
38 views

Differential equation for a list with parameter dependent function

I am having a differential equation: y' = (1 - y) - f[y, mu] y; f is a hysteretic function that depends on y and on the derivative of y: ...
8
votes
3answers
353 views

Bug: Wrong results from NSolve on coupled polynomials. WorkingPrecision->Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
3
votes
0answers
86 views

Constructing the coefficient matrix in discretization of a PDE

In order to solve the following two dimensional PDE $$\frac{\partial u(x,y,t)}{\partial t}-\frac{1}{2} \sigma _1^2 x^2 \frac{\partial ^2u(x,y,t)}{\partial x\, \partial x}-\frac{1}{2} \sigma _2^2 y^2 ...
2
votes
1answer
196 views

Maximized value of a function as an additional constraint on a variable

I want to maximize a function $f(b, h)$ with respect to its arguments and subject to some additional constraints. If these constraints are satisfied, $f$ is increasing in $h$. I then want to find an ...
0
votes
1answer
55 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
0
votes
1answer
37 views

LinearSolve on non-square matrices?

I just came across a strange behaviour for LinearSolve (on Mathematica 8.0.0.0). Consider the following definitions: ...
3
votes
1answer
364 views

Wrong result of simple math calculation. Is it possibly a bug of the program? [closed]

I encounter the following issue accidentally (shown in the screenshot) which is very odd to me. The output[4] and [5] is obviously wrong. But with the input value of 991.91, it turns out to be right ...
3
votes
3answers
115 views

Chopping matrix elements, real or imaginary

An undesired shape of a matrix has the following form: which is created by ...
6
votes
1answer
168 views

Trouble with shooting method for a 4th-order differential equation

I'm trying to solve the following forth-order ODE with the shooting method: $$\frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3 \left[\frac{(xy^\prime)^\prime}{x} \right]^\prime ...
5
votes
0answers
63 views

How does Plus work on machine precision Real arguments?

I thought Kahan's summation method would make a nice example for students to use to think about round-off error [W. Kahan, Pracniques: Further Remarks on Reducing Truncation Errors, Commun. ACM 8  ...
1
vote
1answer
84 views

How can I increase the precision of my computation?

How can I increase precision up to 15 digits for the results (EC, and that of FindRoot) computed below? ...
1
vote
2answers
122 views

Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
3
votes
2answers
104 views

Unexpected behavior from Accuracy

This is my code Table[With[{x = 10^n + 1/17}, N[x, {Infinity, 5}]], {n, 0, 5}] // Column Or like this ...
1
vote
1answer
99 views

Wrong root when using numerical values

I have the following inequality: $$ \sqrt{\frac{a}{2x}}+ \frac{b}{1-\frac{a}{a+\sqrt{a(2bx + a)}}} + \frac{a}{2x\frac{a}{a+\sqrt{a(2bx + a)}}\left(1-\frac{a}{a+\sqrt{a(2bx + a)}}\right)} < f $$ on ...
1
vote
1answer
43 views

System of ODEs - NDSolve issues

I am a self-taught beginner trying to use Mathematica for the first time. If you wouldn't mind, I would like to ask for help with the code I am working on as I keep running into multiple issues when ...
5
votes
1answer
93 views

Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
4
votes
1answer
125 views

Saved InterpolatingFunction behaving badly

Bug introduced in 10 and persists through 10.3.1 or later I created this InterpolatingFunction, and NIntegrate gives an ...
0
votes
2answers
56 views

How to plot the solution of a function while varying a parameter [closed]

I have a function of a single variable that I want to solve numerically for different values of a parameter and then plot the results. I have a general equilibrium model that I can get to a reduced ...
0
votes
0answers
57 views

Error message when using a compiled function in NSum [duplicate]

Below is a simple example to illustrate the problem test = Compile[{{n, _Integer}}, n] Now, Table works fine ...
3
votes
3answers
66 views

EvenQ not working properly on IntegerPart[real number]

Something fascinating is happening at the moment. ...
7
votes
1answer
226 views

Synchrotron Radiation and ListDensityPlot

I'm trying to reproduce the following plots: As described by this blog entry: Synchrotron radiation As you can see in the linked article, the task is essentially to make a ...
1
vote
1answer
295 views

How can I use Mathematica to solve a Stefan Problem using an explicit scheme?

I would like to plot the temperature distribution for a particular case. the problem is stated in the paper, behind a paywall here, summarized as Consider a one-dimensional container of length l, ...
1
vote
1answer
70 views

singularity in boundary value problem

I am trying to solve a non linear differential equation with variable parameter. ...
0
votes
1answer
192 views

How to force numeric evaluation?

I need to evaluate the PolyLog function at some points, but I'm interested in numeric values. E.g. PolyLog[3, 2.7] works fine, ...
2
votes
1answer
69 views

FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
13
votes
2answers
452 views

more numerically accurate inverse matrix

I encountered the following matrix mat = {{2, 2.161209223472559` + 1.682941969615793` I}, {2.161209223472559` - 1.682941969615793` I, 2}} and ...
5
votes
2answers
284 views

Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
1
vote
0answers
41 views

Rescale large numerical factors in rational functions

Given a rational function $$ f(x_1,x_2) = \dfrac{r_1 x_1^2 + r_2 x_2}{r_3 x_1 + r_4 x_2}, $$ with $r_i$ arbitrary real or complex numbers, is there a built-in function to get Mathemtica to rewrite as ...
10
votes
2answers
215 views

Demonstrating the behavior of a function as its independent variable approaches zero

I have several questions regarding the function $$f(x)=\frac{\sqrt{x^2+9}-3}{x^2}$$ that I would like to help my students with in the upcoming semester. Now, the limit as $x\to 0$ is 1/6. ...