A Complete Expression of the Asymptotic Solution of Differential Equation With Three-Turning Points
-
Abstract: In this paper,a second order linear ordinary differential equation with three-turning points is studied.This equation is as follows and λ is a large parameter,but . By using JL function,the complete expression of the formal uniformly valid asymptotic solutions of the equation near turning point is obtained.
-
Key words:
- JL function /
- turning point /
- asymptotic solution
-
[1] 张居铃. 广义Airy函数与具有n个转向点的方程[J]. 应用数学和力学,1991,12(9):845~862. [2] 张居铃. 具有n阶转向点方程的渐近解的完全表达式[J]. 应用数学和力学,1994,15(1):77~86. [3] Moriguchi H. An improvement of the WKB method in the presence of turning points and the asymptotic solutions of a class of Hill equation[J]. J Phy Soc Japan,1959,14(1):1711~1796. [4] Lynn R Y, Keller J B. Uniform asymptotic solutions of the second order linear differential equations with turning points[J]. Comm Pure Appl Math,1970,23(4):379~408. [5] Nayfeh A H. Perturbation Methods[M]. New York: John Wiley & Sons,1973.
计量
- 文章访问数: 2387
- HTML全文浏览量: 107
- PDF下载量: 547
- 被引次数: 0