CAJ | 학술논문

在再生核空间W23[0,1]中给出求解二阶非线性常微分方程组的精确解表达式的方法,此精确解是用级数表示的.证明它的n-截断函数un(x),vn(x)收敛于方程组的精确解u(x),v(x).无论方程组是线性还是非线性,奇异还是非奇异,都可以用本方法求解.算法实例说明此算法是高效的.
재재생핵공간W23[0,1]중급출구해이계비선성상미분방정조적정학해표체식적방법,차정학해시용급수표시적.증명타적n-절단함수un(x),vn(x)수렴우방정조적정학해u(x),v(x).무론방정조시선성환시비선성,기이환시비기이,도가이용본방법구해.산법실례설명차산법시고효적.
The exact solution of two-equation system of second-order nonlinear ordinary differential equations is obtained in the reproducing kernel space W23 [0,1]. The exact solution is represented in the form of series. The n-term approximation un (x), vn (x) are proved to converge to exact solution u (x),v(x). More importantly, the method's implementation requires no additional conditions, whether the equations are singular or non-singular and linear or nonlinear. Examples are presented to demonstrate the reliability and efficiency of the algorithm developed.