A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels

作者：Cai HaoTao^*

来源：Science China Mathematics, 2014, 57(10): 2163-2178.

DOI：10.1007/s11425-014-4806-2

• second kind Fredholm integral equations with weakly singular kernels
• Jacobi-collocation methods
• stability analysis
• convergence analysis

In this work, we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels. Particularly, we consider the case when the underlying solutions are sufficiently smooth. In this case, the proposed method leads to a fully discrete linear system. We show that the fully discrete integral operator is stable in both infinite and weighted square norms. Furthermore, we establish that the approximate solution arrives at an optimal convergence order under the two norms. Finally, we give some numerical examples, which confirm the theoretical prediction of the exponential rate of convergence.

• 出版日期2014-10
• 单位山东财经大学