CAJ | 학술논문

Sine-Gordon方程在非线性光学和生物物理等多个物理问题中有着广泛的应用。本文研究一维Sine-Gordon方程的三次配点法，利用复合高斯求积公式近似内积的一种离散化的H 1-Galerkin方法建立半离散和全离散格式。采用先验估计方法推理了L2, H 1和H 2模最优估计结果。通过Matlab软件编程计算，获得了数值解和真实解的对比结果及误差估计数据。
Sine-Gordon방정재비선성광학화생물물리등다개물리문제중유착엄범적응용。본문연구일유Sine-Gordon방정적삼차배점법，이용복합고사구적공식근사내적적일충리산화적H 1-Galerkin방법건립반리산화전리산격식。채용선험고계방법추리료L2, H 1화H 2모최우고계결과。통과Matlab연건편정계산，획득료수치해화진실해적대비결과급오차고계수거。
Sine-Gordon equation has a wide range of applications in many physical problems, such as nonlinear optics and biophysics. In this paper, a qualocation method is proposed for one-dimensional Sine-Gordon equation, and the semi-discrete and fully discrete schemes are obtained by a discrete H 1-Galerkin method, whose inner product is approximated by the composite Gauss quadrature formula. The optimal error results in L2, H1 and H2-norms are derived by the method of a priori estimates. The comparison between the numerical solution and the exact solution are presented by Matlab software.