摘要
通过对坐标作包含因变量的非线性泛函的变换,以首项渐近解和相应的坐标变换给出原问题的二阶的近似解,并把这种思想进一步推广到更复杂的非线性方程,用较为简洁的方法求得了一类非线性方程的二阶渐近解.
By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functions of dependent variables, their two-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. This paper extends the above method to more complex nonlinear equations. Using a simple and convenient method, we obtain the two-order asymptotic solutions for a class of nonlinear equations.
出处
《纯粹数学与应用数学》
CSCD
北大核心
2005年第1期26-32,共7页
Pure and Applied Mathematics
基金
国家自然科学基金资助项目(10471039)
浙江省自然科学基金资助项目(102009)
浙江省教育厅资助项目(20020305)
湖州师范学院重点科研资助(02101A).
关键词
PLK方法
非线性方程
奇摄动
渐近解
PLK method, nonlinear equation, singular perturbation, asymptotic solution
