Iterated fast multiscale Galerkin methods for Fredholm integral equations of second kind with weakly singular kernels

作者：Long, Guangqing^*; Nelakanti, Gnaneshwar; Zhang, Xiaohua

来源：Applied Numerical Mathematics, 2012, 62(3): 201-211.

DOI：10.1016/j.apnum.2011.12.003

• Integral equation
• Iterated Galerkin method
• Super-convergence
• Fast method
• Weakly singular

We propose iterated fast multiscale Galerkin methods for the second kind Fredholm integral equations with mildly weakly singular kernel by combining the advantages of fast methods and iteration post-processing methods. To study the super-convergence of these methods, we develop a theoretical framework for iterated fast multiscale schemes, and apply the scheme to integral equations with weakly singular kernels. We show theoretically that even the computational complexity is almost optimal, our schemes improve the accuracy of numerical solutions greatly, and exhibit the global super-convergence. Numerical examples are presented to illustrate the theoretical results and the efficiency of the methods.

• 出版日期2012-3
• 单位南宁师范大学