Zakian反演法在求解双曲型方程中的应用  

An Application of Zakian Inversion Method in Solving Hyperbolic Differential Equations

作　　者：王丽[1] 张麟[2] 

机构地区：[1]中国民航飞行学院计算机学院,四川广汉618307 [2]南京大学数学系,江苏南京210093

出　　处：《四川师范大学学报（自然科学版）》2013年第4期530-533,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科研基金联合基金(U1233105)资助项目;中国民航飞行学院面上项目( XM0394)

摘　　要：首先对双曲型方程作Laplace变换得到椭圆型方程,再使用四阶高精度的差分格式并行地求解5个椭圆型差分方程.在求得椭圆型差分方程的近似解后,用Zakian反演法得到双曲型方程在任何时刻的高精度数值解;数值实验表明了此方法十分地有效.By means of Laplace transformation the hyperbolic differential equations are transformed to the elliptic differential equations which can be solved by the fourth order finite difference equations in parallel.After getting the approximate solutions of the elliptic differential equations,we can achieve the numerical solutions with high accruracy in any time for the hyperbolic differential equations by using the Zakian inversion method.At last,we carry out one numerical experiment to indicate that the method in this paper is very effective.

关 键 词：双曲型方程 Zakian反演法 差分方法 

分 类 号：O175.27[理学—数学] O241.82[理学—基础数学]