CAJ | 학술논문

在再生核空间中构造一个新的带有非局部边界条件的非线性四阶奇异边值问题的对称正解的迭代算法.证明近似解及其k(k=l,2,3,4)阶导函数一致收敛于精确解及其各阶导函数.给出的数值算例验证方法的有效性.所提出的算法对于求解线性与非线性积分边界问题是有效的.
재재생핵공간중구조일개신적대유비국부변계조건적비선성사계기이변치문제적대칭정해적질대산법.증명근사해급기k(k=l,2,3,4)계도함수일치수렴우정학해급기각계도함수.급출적수치산례험증방법적유효성.소제출적산법대우구해선성여비선성적분변계문제시유효적.
A new constructive iterative method is employed to obtain the symmetric positive solution for nonlinear singular BVPs of fourth-order with nonlocal boundary conditions in the reproducing kernel space. The approximate solution are proved to converge uniformly to the exact solution with all its k-order (k = 1,2,3,4) derivatives. Numerical examples are given to verify the strength of the method. It is worthy to note that the new method can be used as a very accurate algorithm for solving linear and nonlinear integral boundary problems.