A Nystrom method for integral equations with fixed singularities of Mellin type in weighted L-p spaces

作者：De Bonis M C^*; Laurita C

来源：Applied Mathematics and Computation, 2017, 303: 55-69.

DOI：10.1016/j.amc.2017.01.027

• Mellin kernel
• Integral equation of Mellin type
• Nystrom method
• Lagrange interpolation
• Gaussian rule

We consider integral equations of the second kind with fixed singularities of Mellin type. According to the behavior of the Mellin kernel, we first determine suitable weighted L-P spaces where we look for the solution. Then, for its approximation, we propose a numerical method of Nystrom type based on a Gauss-Jacobi quadratura formula. Actually, a slight modification of the classical procedure is introduced in order to prove convergence results in weighted LP spaces. Moreover, a preconditioning technique allows us to solve well conditioned linear systems. We show the efficiency of the proposed method through some numerical tests.

• 出版日期2017-6-15