CAJ | 학술논문

研究了带弱奇异核分数阶偏积分微分方程的初边值问题。首先，在空间方向用谱Galerkin方法得到空间半离散格式，然后证明了该格式的稳定性和误差估计，收敛率体现了“谱精度”；在时间方向采用了中心差分，积分项采用了Lagrange内插法进行离散得到时空全离散格式。最后用数值实验检验了该方法的有效性，同时也确保了理论分析的准确性。
연구료대약기이핵분수계편적분미분방정적초변치문제。수선，재공간방향용보Galerkin방법득도공간반리산격식，연후증명료해격식적은정성화오차고계，수렴솔체현료“보정도”；재시간방향채용료중심차분，적분항채용료Lagrange내삽법진행리산득도시공전리산격식。최후용수치실험검험료해방법적유효성，동시야학보료이론분석적준학성。
Spectral-Galerkin methods for the initial-boundary value problem of the fractional order partial integro-differential equations with a weakly singular kernel is considered .First, in space direc-tion, the semi-discrete scheme is derived by using spectral-Galerkin methods , the stability and error esti-mates of the scheme are proved , the convergence rate shows “spectral accuracy”.Then, in time direc-tion by the center differential , the integral term is treated by the Lagrange interpolation , the fully discrete scheme is achieved based on the semi-discrete scheme.Finally, a numerical experiment is presented to demonstrate the effectiveness of the method and confirm the theoretical results .