陈烨远^*

（  同济大学数学系；  ）

摘要： 本文提出一种使用拟线性有理配点法求解具有边界层在一端（左端或者右端）或具有内部过渡区域的两点边值问题的非线性奇异摄动问题。通过使用非线性方法，非线性问题被一系列线性问题所代替。退化问题的解（令原问题）被初始逼近所代替。利用基于Sinh变换的有理配点法用来求解一系列线性问题。此方法提供了与其他方法相同的精度逼近，并且更加有效。通过数值算例演示了这种方法的高精度和高效性。
关键词： 非线性奇异摄动问题；有理配点法；Sinh变换；边界层；内部过渡区域

Chen Yeyuan ^*

（  Department of Mathematics, Tongji University；  ）

Abstract： A quasilinearization rational collocation method is presented for solving some non-linear singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right)point or with an internal transition region. By using a quasilinearization technique, the non-linear problem is replaced by a sequence of linear problems. The solution to the reduced problem (the given problem by putting ) is taken as the initial approximation. Rational collocation method based on Sinh transform is applied to solve the sequence of the linear problems. The method produces the same accurate approximations as other numerical methods, but it is more efficient. The high accuracy and efficiency of the method are illustrated by the numerical examples.

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