MATLAB GUI for computing Bessel functions using continued fractions algorithm

Abstract

Higher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting values and normalization constants to evaluate Bessel functions. The continued fractions algorithm directly computes each value, keeping the error as small as possible. Both methods respect the stability of the Bessel function recurrence relations. Here we outline both methods and explain why the continued fractions algorithm is more efficient. The goal of this paper is both (1) to introduce the continued fractions algorithm to physics and engineering students and (2) to present a MATLAB GUI (Graphic User Interface) where this method has been used for computing the Semi-integer Bessel Functions and their zeros.

Animation with Algodoo: a simple tool for teaching and learning Physics

“…Furthermore, we note that the motion is symmetric with respect to the vertex of the parabolic trajectory, and also that the horizontal component of velocity remains constant throughout the route. These effects are predictable, by a detailed analysis of Equations ( 1) and (3).…”

“…In the last decades, due to technological advancement, the numbers of tools that aim to facilitate teachers and students in the educational process have grown. Nowadays, an educator has the opportunity to demonstrate, in class, the evolution of physics equations and systems, by varying the parameters in real time, through commercial softwares as Wolfram Mathematica [1,2], Matlab [3] and Labview [4][5][6]. In other cases, simulations and/or animations [7][8][9][10][11] can be created, based on different computer languages, data acquisition boards to make automatization of experimental data [12][13][14] and software like Modellus [15][16][17][18][19][20], which is a free application that allows us to use mathematics to create or explore models interactively.…”