数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2012年
2期
179-187
,共9页
Legendre-Laguerre耦合谱元法%三阶微分方程%半直线
Legendre-Laguerre耦閤譜元法%三階微分方程%半直線
Legendre-Laguerre우합보원법%삼계미분방정%반직선
Legendre-Laguerre coupled spectral-element method%third-order differential equation%half line
针对建立在半直线上的三阶微分方程,提出Legendre-Laguerre耦合谱元法.通过构造满足试探函数空间和检验函数空间的基函数,分解得到的线性系统的系数矩阵是稀疏的,可以有效地进行求解.数值例子验证了方法的有效性和高精度.
針對建立在半直線上的三階微分方程,提齣Legendre-Laguerre耦閤譜元法.通過構造滿足試探函數空間和檢驗函數空間的基函數,分解得到的線性繫統的繫數矩陣是稀疏的,可以有效地進行求解.數值例子驗證瞭方法的有效性和高精度.
침대건립재반직선상적삼계미분방정,제출Legendre-Laguerre우합보원법.통과구조만족시탐함수공간화검험함수공간적기함수,분해득도적선성계통적계수구진시희소적,가이유효지진행구해.수치례자험증료방법적유효성화고정도.
Legendre-Laguerre coupled spectral-element method is proposed to numerically solve linear third-order differential equations on the half line. By choosing appro- priate trim and test basis functions, the problems are decomposed into some sparse linear systems which can be solved easily. Numerical experiments are given to confirm the effec- tiveness and high-accuracy of the method.
