【摘要】 充分运用再生核的技巧,给出了一类常微分方程边值问题的精确解的级数形式表达式,为了得到边值问题的近似解,描述了迭代解法并进行了理论分析。本方法的优点在于构造了新基底,绕过了求施密特正交化的麻烦。通过数值例子验证了该方法不仅有效而且高精度。更多还原

【Abstract】 A series representation of exact solutions of a class of boundary value problems of ordinary differential equations is given by making good use of reproducing kernel techniques. For getting the approximate solution,A iterative method is presented and its theoretical analysis is done. The advantage of the method lies in employing a new basic function and avoiding to the Schmidt orthogonalization. Results of some numerical examples have demonstrated that the proposed approach is not only effectiveness but also possessing good accuracy.更多还原