摘要
针对Havelock型三维移动脉动源格林函数(3DTPS)的高振荡性这一主要计算难点,给出了计算高振荡积分的一种新方法。根据振子函数是否存在驻点,综合运用Filon方法和三次样条函数插值的方法进行计算,并提出了一种不同于Lobatto法则的新变换来消除无穷间断点,从而简化了高振荡积分的计算,提高了其适应性。
Aim at difficulty of highly oscillatory integral in the Havelock form of Green's function for 3 D translating-pulsating source(3 DTPS) hinders the numerical integration efforts, this paper proposes a new method for the calculation of highly oscillatory integral. According to if oscillator function has stationary point or not, Filon method with cubic spline as interpolating function is used alone or together with usual numerical integration method. Besides, a new substitution different from Lobatto rule is introduced to eliminate the singularity of infinite discontinuity, which can make the numerical calculation more flexible and simplify the highly oscillatory integral, and improved its adaptability.
引文
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