High Oscillating Integral Levin And Legendre Polynomial Recursive Iteration Method Is Used To Solve The Research

Highly oscillatory function integral is one inevitable difficulty in some application areas like physics, chemistry, engineering. This essay is aimed at giving some numerical computation methods through making studying on highly oscillatory function integral methods which rapidly develop in recent years.In the first chapter, this paper gives the definition of highly oscillatory function and some usual forms in general, and then arrays some applications of highly oscillatory function integral and some effective arithmetic.In the second chapter, this paper introduces Levin method in response to solve highly oscillatory function integral, and gives Levin iteration method of many dimensions, examples and error analysis.In the third chapter, this paper introduces definition and basic properties of Legendre polynomial and gives recurrence formula of Legendre polynomial to solve highly oscillatory function integral, examples and error analysis.