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10
votes
2answers
725 views

Why is Mathematica destroying this graph?

Here I have a picture of a function I graphed: reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]]; Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic] And here is ...
0
votes
0answers
26 views

Implementing more accurate boundary conditions in NDSolve

I want to solve a second order differential equation numerically. The boundary conditions are needed to be imposed at z=0 and at ...
3
votes
1answer
45 views

My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
2
votes
3answers
189 views

What's the proper way to 'cut out' an irrelevant part of an integral, so I don't run into problems with precision?

I'm doing a numerical integration that involves an integrand with a few exponentials whose values over the integration region range enormously. I'm really only interested in the part of the range that ...
0
votes
1answer
61 views

WorkingPrecision and AccuracyGoal for using with NIntegrate

I'm modeling a quantum tunneling barrier. Because I want to express my quantities in mks units, that means that some of the variables I'm using are pretty small (10^-9). I use NIntegrate for part of ...
0
votes
0answers
94 views

Why do Precision and Accuracy level off in this calculation?

I am confused by this behavior, where Precision and Accuracy seem to reach a bottom and deteriorate no further as I perform more iterations on this calculation. Have I misunderstood something about ...
4
votes
0answers
73 views

Improve Accuracy of FindRoot

This is a follow up question to an earlier questions I asked. The link is: Product of $N\ 2 \times 2$ matrices and subsequently solving an equation dependent on the product As I am new here, I am not ...
6
votes
0answers
129 views

Why has Version 10.3 precision reduced?

In version 7.0.1.0 and versions 10.0 and 10.1 the following is produced: ...
0
votes
0answers
38 views

Maintaining working precision in my program

I am badly stuck with this program I am writing. I want output of program below to be precise up to 25 digits after decimal point. I am supplying all inputs with precision 25. But after each iteration ...
0
votes
2answers
80 views

Exact calculating the multiply of two real [closed]

As the machine calculate,the exact calculating with real number have some problem to puzzle me long time.We know the 0.142*0.36523=0.05186266 is exactly equalized ...
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 ...
13
votes
2answers
535 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 ...
1
vote
0answers
77 views
1
vote
1answer
64 views

Accurate Integration of 2D interpolating function with weighting

I want to integrate a 2D interpolating function received from NDSolve[]. To illustrate my problem I will give a simple example: ...
7
votes
2answers
258 views

NIntegrate fails to converge under almost any PrecisionGoal, MinRecursion etc. How can I trust the result?

I have been getting some ideas by reading other related questions in the forum, but the integral I have to do is not converging in many cases. The integrand is of the form: ...
0
votes
1answer
58 views

Problem with precision of fraction numbers

I have tried to take a series of harmonic numbers using Mathematica and its precision but there has been an issue. So far when I computed the sums at a whole numbers using a precision of 100 digits I ...
1
vote
0answers
71 views

Problem with calculating Harmonic Numbers

I have tried to take a series of Harmonic Numbers using mathematica but there have been issues in calculations. So far when I computed the sums at a small value range such as ...
3
votes
1answer
73 views

In NMinimize, how can I efficiently handle NIntegrate errors for non-integrable functions?

I am using NMinimize to find parameters that minimise the integral of a function in the least squares sense: ...
4
votes
2answers
77 views

Is there a way for accuracy backtick notation to accept variable inputs?

Backtick notation uses 1.0``20 to give 1 with 20 places of accuracy after the decimal point. But what I want is ...
2
votes
1answer
98 views

Funny behavior when computing dot product of coefficients with high-order polynomials

I have a similar problem to Funny behaviour when plotting a polynomial of high degree and large coefficients. However, the thing being evaluated is not just a polynomial but a dot product of some ...
6
votes
1answer
157 views

Accuracy of Grad-Shafranov PDE's NDSolveValue over implicit region

Context I need to solve for the toroidal flux of the magnetic field above an accretion disc. For this purpose, I define the region over which the flux is non zero, ...
12
votes
1answer
262 views

How to add AccuracyGoal and PrecisionGoal options in a numerical function?

There are many built-in functions that contain AccuracyGoal, PrecisionGoal and ...
4
votes
0answers
391 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
0
votes
1answer
54 views

If statement for evaluating small values

I have a simple calculation which I am trying to use if condition to evaluate summation of some values, here's a code; ...
4
votes
1answer
94 views

NDSolve returns asymmetric solution to a symmetric equation

I am trying to find the potential of a conducting cylindrical electrode by solving the Laplace's equation. Both, the boundary conditions and the equation are symmetric w.r.t. the change $r\to-r$. ...
1
vote
1answer
215 views

Precision while calculating Fourier transform

I'm trying to understand how precision works in Mathematica. Particularly I'm calculating discrete Fourier transform using the Fourier function and calculating it ...
6
votes
0answers
75 views

Negative accuracy numerics ( 0``-128 notation )

What does it mean to have a negative accuracy number? I understand 0``128 to mean "the number zero to 128 decimal points". Mathematica corroborates this: ...
3
votes
3answers
326 views

3D Gamma function

I try to plot the following function: Plot3D[Gamma[1+0.5*(n+m)]/Sqrt[Gamma[1+n]*Gamma[1+m]],{n,0,1000},{m,0,1000}] I expect that for m=n and near to it the value ...
8
votes
1answer
420 views

How trustworthy is NMaximize?

Suppose I solve a constrained optimisation problem using NMaximize. How confident can I be of the accuracy of the result? For concreteness, suppose that F,G are ...
2
votes
2answers
278 views

How to get the digits after the decimal point

I have N[Sqrt[2], 8] which outputs 0.4142136 How do I get the 4142136 part out of it? I ...
3
votes
1answer
220 views

Precision of NIntegrate

At the moment I am considering a "difficult", highly-oscillatory integral in Mathematica. It calculates the integral without any complaints. However, I am also trying out a numerical method with which ...
8
votes
1answer
212 views

Numerical Integration different in Mathematica version 9 and 10 with same options

I have noted that the same function with the same settings gives me different results in Mathematica version 9 and 10. This involves integrating numerically interpolating functions and so on. Here a ...
0
votes
2answers
142 views

Accuracy and WorkingPrecision

Observe that ...
10
votes
2answers
902 views

Floating point operations — division vs multiplication; how do they affect accuracy?

Given two functions: f[x_] := x ((x + 1)^(1/2) - x^(1/2)) g[x_] := x/((x + 1)^(1/2) + x^(1/2)) Which one is more accurate? Side note: If you could explain why, ...
1
vote
1answer
108 views

Option: number of digits

The command NestList[Cos, 1.5, 10] produces the list: ...
3
votes
1answer
62 views

Deferent results depending on the input form of the matrix [duplicate]

Why is it so, N[Eigenvectors[{{1., 0.5, 4.}, {2., 1., 2.}, {0.25, 0.5, 1.}}]] returns: ...
0
votes
0answers
71 views

Handling Accuracy and Simplifying

I have the following problem. I have a system of non-linear equations that I log-linearize around a certain point, let's call it point A, using a function that I ...
1
vote
1answer
85 views

User defined functions and decimal places displayed

I have a couple of complicated user-defined functions, one which calls the other, and I wish to control the number of decimal places displayed when I call the "mother" function. I have tried the ...
1
vote
0answers
148 views

the default option of NDSolve

How should I find out what the default value of Accuracy and Precision is in the NDSolve? I have a pde that when I asked it to solve for me the equation with a special Accuracy and precision it gave ...
36
votes
3answers
7k views

Understanding differences between Maple and Mathematica in examples picked by Maplesoft

I am reading the document How Maple Compares to Mathematica. On page 15 there is an example where Mathematica produces wrong results. Does anybody know why? MAPLE: MATHEMATICA: Also on page 17 ...
1
vote
1answer
92 views

How to solve the warning problem and obtain real roots without imaginary part?

I am trying to solve a equation with Newton's method via FindRoot, and the codes are: Define the functions: ...
0
votes
1answer
59 views

How to check the decimal accuracy of result? [duplicate]

I am trying to check if the result is enough accurate to use. I need an accuracy of 10^-6 from some numerical method. Something like root finding algorithm. But how do I check that in mathematica? I ...
1
vote
1answer
195 views

How can we ensure the result of Mathematica is exactly correct?

This is an example, I plot a function and find it has a defect when x approximates 400. Plot[Cos[.3 x] Exp[-0.01 x], {x, 0, 1000}, PlotRange -> All] Another ...
8
votes
1answer
115 views

Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
1
vote
1answer
84 views

Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
3
votes
1answer
512 views

N[number, 100] does not give 100 decimal places [duplicate]

Please look at this computations: a = N[Sqrt[2], 20]; N[a^2, 100] The output is 2.0000000000000000000, which is apparently not $a^2$ to 100 decimal places. ...
1
vote
0answers
256 views

Choosing PrecissionGoal and AccuracyGoal for decomposed integral with NIntegrate

Assume I have a complicated integral $I$ which can feature all kinds of difficulties like infinite interval, rapidly oscillatory integrand, integrable singularities and numerically almost singular ...
7
votes
1answer
232 views

Law of Cosines to determine angle change along spiral

The Spiral I'm trying to place circles along the outside of an Archimedean spiral. Shown below: ...
4
votes
0answers
140 views

Tools for Stability/Automatic Error Analysis in Mathematica

I have a longer analytic expression in several variables containing special functions and others. Does Mathematica bring tools - or are there any packages - to examine the stability when I evaluate ...
5
votes
1answer
698 views

How to improve the solution of a double pendulum system

First, the code: ...