# Tagged Questions

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

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### Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions

Bug introduced in 7.0 or earlier and persisting through 10.4.1 This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore ...
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### Wrong numerical results from LegendreP

{Cos[Pi/180] // N, LegendreP[46, 0.9998476951563913`], LegendreP[46, Cos[Pi/180]] // N} give ...
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### Why does N[1.000 01, 10] return 1.00001, but N[1.000 001, 10] returns only 1.?

Why is it so? When I ask for N[1.00001, 10] I get quite reasonably 1.00001 But when I ask for ...
7k views

### About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
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### Solving a matrix differential equation using RBFs

Michael Kelly in the paper http://www.mathematica-journal.com/2010/02/evaluation-of-financial-options-using-radial-basis-functions-in-mathematica/, discussed how to apply Mathematica for solving the ...
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### Why does NDSolve and NIntegrate not give the same result?

I have plotted solution of two equivalent equations one in Integral form (right chart) the other in Differential form (left chart) using NDSolve and NIntegrate but they give me completely different ...
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### 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 ...
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### How can use Table for two functions obtained from NDSolve? [on hold]

I have obtained a numerical solution using NDSolve for two functions a(x) and b(x). how do I use Table to make a list of a(x) vs b(x) values. is it simply Table[{a(x),b(x)},{x,0,100}] or should I use ...
458 views

### Numerical instability in cosh and sinh - integral functions [duplicate]

I'm trying to calculate the function: CoshIntegral[x] Sinh[x] - Cosh[x] SinhIntegral[x] Unfortunately Mathematica seems to hit a point (x~20) and things become ...
242 views

### Strange phenomenon occurring in analytic integration result involving Bessel functions

For the following integral, Integrate[x^2 Exp[-a x^2 - b x^4], {x, -∞, ∞}, Assumptions -> {a > 0, b > 0}] Mathematica gives the following analytic ...
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### FindMinimum step size too small

I'm running a simulation of an electromagnetic system using Radia, an external code that is run from Mathematica. I want to use FindMinimum to determine some ...
170 views

### Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
501 views

### Problem with FindRoot applied to functions

I am having difficulty with the error "is not a list of numbers with dimensions..." when using FindRoot (and other numerical routines in Mathematica) to solve equations numerically when the argument ...
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### High Precision Plots of Eisenstein Series [closed]

When plotting the Eisenstein Series (great information here Eisenstein Series in Mathematica?) you observe highly non-trivial branch cut behavior close to the real axis. This makes the numerics break ...
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### Find absolute minimum with NMinimize method

Hello Mathematica Bloggers. I'm facing up a problem with NMinimize[] in Mathematica. I need to find the best fit for some ...
4k views

### how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...