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

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2
votes
4answers
163 views

Padding and formatting within BaseForm

I find using BaseForm to be a little tricky. For example, if you use BaseForm and then do some additional operation all the numbers turn back into base 10, so you have do BaseForm as the "last step". ...
2
votes
2answers
137 views

Incorrect numerical derivative of function that uses FindRoot

I am trying to plot the derivative of function g[x] below where g[x] is defined as the root of another equation. However, I am ...
0
votes
1answer
84 views

Truncate a fractional value to particular number of bits?

If I have a fractional value, how can I truncate (not round) that to a certain number of bits, like 8? For example, for Pi 3.141569265359... the fractional part is 0.141569265359... ...
2
votes
1answer
115 views

Read C-formatted hexadecimal numbers?

I have a lot of 32-bit numbers in hexadecimal symbolized as they are in C (for example, 0x1230abde). How can easily read these in Mathematica?
5
votes
4answers
340 views

Display a number in Mathematica 9 in periodic form

I want to display a rational number in Mathematica in periodic style. PeriodicForm isn't working anymore. It worked in Mathematica 5 and now I'm using Mathematica ...
0
votes
0answers
140 views

NMaximize, restart

I have to optimize some contrained functions and I am trying to use NMaximize. I have the following problem (see code below). I use ...
6
votes
1answer
190 views

Iteration process involving several functions

I would like to carry out a following iteration process: Apply function f1[a_,b_,c_,d_] to a starting list l1={a1,b1,c1,d1}, ...
1
vote
3answers
123 views

automatic processing of numerical results in `Plot`

First I want to solve an equation $F(x,y)=0$ for $y$ by supplying a value of $x$. (suppose obtaining the analytic form of $y(x)$ is too difficult) Then I want to plot root $y$ (numerically calculated) ...
0
votes
0answers
99 views

Getting increased accuracy for roots of determinant

I have a matrix $a(\kappa)$ from which I am trying to determine $\kappa$ by using the equation $det(a(\kappa)) = 0$. The matrices I deal with are on the order of 100 X 100 to 500 X 500. Originally I ...
3
votes
1answer
326 views

Numerical solution of Bessel-like equation using NDSolve

I need to calculate solution of Bessel-like equation having general form: $\frac{d^2F}{dr^2}+\frac{1}{r}\frac{dF}{dr}+Q(r)F(r)=0$. Problems come from the points near $r=0$ leading to numeric errors. ...
1
vote
1answer
101 views

Passing f[x][[1]] to FindRoot [duplicate]

FindRoot seems to fail for most examples of the form f[x_?NumericQ] := {x - 3 , x^3}; FindRoot[f[x][[1]], {x, 3}] ...
1
vote
3answers
270 views

Can plot a function, NSolve takes too long

I'm new to Mathematica, so maybe mine is an easy to solve issue, but I haven't been able to figure it out. I have a series of linear ODEs I solve using for: ...
2
votes
1answer
230 views

Animated Wave Propagation using Fourier & InverseFourier

This is a continuation off of previous help on the first part of my project: fourier issue arising from input miscommunication Now I want to go one step further in the current code. Here's the code ...
3
votes
1answer
222 views
3
votes
3answers
426 views

Implementing Newton's method

I have this question on coding Newton's method in Mathematica. I have some code to go by but I have no clue if it's computing the functions in the right order. The book is the numerical methods ...
12
votes
2answers
261 views

Why do NumberForm and Round apparently use different tie-breaking methods?

When rounding numbers (for example, rounding a real number to the nearest integer), the "round to nearest" rule is usually used. For example, 1.4 is rounded down to 1 and 1.6 is rounded up to 2. ...
1
vote
1answer
142 views

Using NMinimize Properly

I'd like to find the point on a Bezier curve that's closest to some other point. The tricky thing is that because Bezier curves can loop around, the distance function can have multiple local minima ...
0
votes
0answers
130 views
12
votes
1answer
737 views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
1
vote
3answers
409 views

How many iterations of Newton's method are needed to achieve a given precision?

Consider using Newton's method to solve the equation $arctan(x) = 0$. Using an initial guess of $x_0 = 1/2$ produces a sequence that converges rapidly. After $8$, iterations, $x_8$ is accurate to well ...
7
votes
1answer
86 views

Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
3
votes
1answer
96 views

obtaining real roots of negative numbers in a long expression [duplicate]

I have a complicated symbolic expression which contains many terms like $(a/(a-2))^{1/m}$, where $a/(a-2)$ could be positive or negative after replacement. I only need the real root after ...
9
votes
1answer
352 views

ParallelEvaluate for function minimization

Is there a parallelized version of a minimization routine available in Mathematica? The objective function is non-linear and the gradients have to be numerically computed. Every function evaluation ...
5
votes
1answer
396 views

Function to subdivide interval into n evenly-spaced points

[This post needs better tags than I could come up with. Edits to the tags would be particularly welcome.] I realize that it is trivial to define a function that takes an interval (i.e. two ...
4
votes
2answers
222 views

Quickly reducing the number of decimal digits for a set of real numbers

How can I quickly convert a number with $n$ decimal points to a number of with $m$ decimal points? Round works, however, it is slower than I would like. This ...
5
votes
0answers
209 views

NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
1
vote
0answers
42 views

Rounding to the nearest decimal [duplicate]

If I have a bunch of numbers in a list {1.435243523432,2434.2321321412,5.8239897,...}, without multiplying everything by some power of ten and then dividing by that ...
0
votes
2answers
105 views

Error in the result

I want solve the following equation: $ x''(t) + 9 x(t) = Cos(3t) ,\; t \in [0,10] $ $ x(0)= x'(0) =1$ I have to use the Explicit Euler method and a partition of the interval in $N+1$ ...
4
votes
4answers
324 views

How to find the maximum of a function on a set of discrete points?

How to find the maximum of a function on a set of discrete points? For example, what is the best way to find the maximum of ...
2
votes
1answer
237 views

How to make Mathematica try harder to perform symbolic comparisons?

(I suspect this question is a duplicate, but I didn't find a sufficiently similar question with an answer to it.) I'm having trouble with comparisons of symbolic ...
8
votes
1answer
148 views

Exp of big negative numbers [duplicate]

I noticed that Exp have a strange behaviour with big negative numbers ...
0
votes
0answers
177 views

How to implement an implicit iterative method for solving SDEs?

I wish to numerically solve the Black-Scholes SDE as follows $$ \begin{array}{lll} dX(t)&=&\mu X(t)dt+\sigma X(t)dW_t, \ \ \ 0\leq t\leq1,\\ X(t_0)&=&X(0), \end{array} $$ with the ...
1
vote
1answer
152 views

Domain restrictions for NMaximize

I am trying to solve a maximization problem, where my variable can only take a limited number of values. (Probably) the easiest example would be ...
2
votes
1answer
197 views

How can I numerically solve for fractional functions and fractional derivatives?

I would like to plot fractional functions. Say $f=(\sin)^{1/2}(x)$. By that I mean that $f(f(x)) = \sin(x)$. Similarly I can define a half-derivative to be an operator such that $H[H[f(x)]] = ...
7
votes
2answers
400 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
3
votes
0answers
103 views

Strange NSum behavior

If I do: NSum[(i + 1)/(i + 2) LegendreP[i, 0] LegendreP[i, 0], {i, 0, Infinity}] I get: 1.25216 If I do: ...
2
votes
1answer
336 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: ...
2
votes
1answer
94 views

Use Mathematica to determine the falling law

We have a one-variable equation $\rho(R)$ where ρ = (14656.4+277.526*R^2)/(45.9225+R^2)^{5/2} + 0.370036/(R*(0.25+R)^3) This equations describes the evolution of ...
4
votes
1answer
104 views

Strange behavior of Mathematica regarding calculation time

Today I witnessed the following strange behavior of Mathematica, when it comes to calculation time involving larger nested lists. The following is the short example that I setup, I am sure one can ...
-1
votes
1answer
245 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 ...
4
votes
0answers
723 views

Numerically solving system of partial differential equation

I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
4
votes
1answer
307 views

Counting the number of operations performed during a calculation

I need to know how can I count the number of operations performed during a calculation of a CompoundExpression. In some of these expressions there are ...
0
votes
1answer
102 views

Question with ParametricNDSolveValue

When solving the following system: ...
8
votes
1answer
1k views

Computation of Hankel Transform using FFT (Fourier)

To address circular symmetric cases of 2D Fourier Transformations the so called Hankel Transform can be applied (for a detailed derivation of the relation between the 2D Fourier transform and the 1D ...
3
votes
2answers
272 views
9
votes
1answer
101 views

Apply N only outside a certain function

1 + f[1] // N gives 1. + f[1.] I don't want the argument of f evaluated by N; I ...