# Tagged Questions

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729 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 ...
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 ...
190 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 ...
45 views

### My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
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 ...
63 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 ...
96 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 ...
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: ...
76 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 ...
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: ...
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 ...
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 ...
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 ...
540 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 ...
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 ...
77 views

### $\tt PrecisionGoal$ and $\tt AccuracyGoal$ making the solution less accurate?

I am having this differential equation: ...
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: ...
261 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: ...
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 ...
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 ...
142 views

Observe that ...
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### 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: ...
612 views

### Setting the Accuracy of calculations

I need to optimize an expression that involves a number of trigonometric functions and Exp[]. How do I make sure that all my calculations have an accuracy of ...
77 views

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

Backtick notation uses 1.020 to give 1 with 20 places of accuracy after the decimal point. But what I want is ...
327 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 ...
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 $r\to-r$. ...
160 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, ...
264 views

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

There are many built-in functions that contain AccuracyGoal, PrecisionGoal and ...
170 views

### Is there a way to get BSplineFunction beyond MachinePrecision?

I have been using BSplineFunction (Mathematica 8) to generate a smooth representation of some data, which I might then do some further processing on. As I ...
398 views

### Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
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; ...
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 ...
217 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 ...
221 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 ...
75 views

### Negative accuracy numerics ( 0-128 notation )

What does it mean to have a negative accuracy number? I understand 0128 to mean "the number zero to 128 decimal points". Mathematica corroborates this: ...
421 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 ...
280 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 ...
214 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 ...
904 views

### Floating point operations â€” 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, ...
108 views

### Option: number of digits

The command NestList[Cos, 1.5, 10] produces the list: ...
699 views

### How to improve the solution of a double pendulum system

First, the code: ...
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 ...
150 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 ...
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: ...
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 ...
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 ...
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. ...
84 views

### Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
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. ...
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 ...