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The Bessel transform numerical integration algorithm

Author: MoPingHua
Tutor: XiangShuHuang
School: Central South University
Course: Applied Mathematics
Keywords: Bessel transform Asymptotic method Levin-Type method High oscillation function integral
CLC: O241.4
Type: Master's thesis
Year: 2006
Downloads: 141
Quote: 3
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Abstract


Containing Bessel function of integral calculation is a hot topic in physics, chemistry and engineering applications , but in a lot of cases , Bessel functions J_m (rx) was the oscillatory high , so it is also a difficulty . This paper aims to study , given the rapid development in recent years of high oscillating function integration method efficient numerical method for solving such integral issues . Summary of the first chapter of the high oscillation function numerical integration , especially those containing the classic Bessel transform numerical integration methods and the latest development and pointed out that the successes and shortcomings . Chapter II , is committed to solve the Bessel function integral two new methods - asymptotic method and Levin-type method , and gives the error estimates and numerical example proved it to solve a new Bessel function integral efficient method . The third chapter , containing Bessel functions of the newly proposed numerical integration methods based the Matlab algorithm design research , to provide users with a convenient computing such integral , integral tool for visualization . In addition , in the second chapter asymptotic integration method based on a limited range of the integral is extended to an infinite range , given the new method of calculation of the generalized Bessel function integral .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Numerical integration method,numerical differentiation
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