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

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2
votes
1answer
179 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
201 views
3
votes
3answers
275 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
224 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
120 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
125 views
12
votes
1answer
611 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
358 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 ...
0
votes
0answers
60 views

Is mathematica able to count all results?

I have N variables, say $V_1, V_2, ..., V_n$. and I have several logical conditions like $[(V_1 > V_2) \cap (V_2 + V_3 > V_1) \cap (V_1*V_1 > 2*V_2)] \cup [..]$ You can consider they are in ...
7
votes
1answer
80 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
90 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
291 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 ...
4
votes
1answer
242 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
181 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
159 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
40 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
96 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
297 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
213 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
134 views

Exp of big negative numbers [duplicate]

I noticed that Exp have a strange behaviour with big negative numbers ...
0
votes
0answers
163 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
124 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
169 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
363 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
100 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
291 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
100 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
207 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
620 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
254 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
86 views

Question with ParametricNDSolveValue

When solving the following system: ...
8
votes
1answer
775 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
269 views
9
votes
1answer
99 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 ...
14
votes
2answers
137 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...
0
votes
0answers
401 views

How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
3
votes
2answers
292 views

Numeric calculation of Hessian

I want to calculate the Hessian matrix for a function that can only be evaluated numerically. So far, I have the following (where f is just for testing): ...
0
votes
1answer
154 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 ...
-4
votes
1answer
181 views

findroot, derivative in defined functions

I apologize for my unclear question, I will write it in a more detailed way. I first define: ...
11
votes
1answer
696 views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
0
votes
0answers
141 views

Assigning numerical values to constants results in complex coefficients in Equations of Motion

I am using Mathematica to get the Equations of Motion (EOM) for a mechanical system (using Lagrangian Mechanics). While I get the EOM in symbolic form, on introducing the following code for assigning ...
1
vote
1answer
123 views

FindRoot equation-variable mismatch

I cannot figure out why FindRoot doesn't work and returns this error: The number of equations does not match the number of variables in ... My problem: drawing ...
2
votes
1answer
198 views

Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
2
votes
1answer
126 views

Strange behavior when replacing variables by numerical values [duplicate]

I have a rather complicated function with parameters {a, b, c, d, e, f, k}, and I'd like to know its behavior as a function of k alone given other parameters, so I try the following code: ...
26
votes
1answer
738 views

Numerics with Mathematica

From time to time, I would like to use Mathematica purely numerically, e.g., plotting a function which is defined as an integral which cannot be solve analytically or a solution of a differential ...
0
votes
2answers
85 views

Generating equally distributed voxel points based on a given point

I have a list of seed points that each of them indicates the bottom-left value of a voxel. In order to improve the accuracy of my function, I need to equally sample my points and apply my functions ...
-1
votes
2answers
254 views

Performance of numerical optimization with triple integral [closed]

I'm trying to solve a numerical optimisation that looks something like this: ...