In this paper a new modified Nyström method is proposed to solve linear integral equations of the second kind with fixed singularities of Mellin convolution type. It is based on the Gauss-Radau quadrature formula with a suitable Jacobi weight. The stability and convergence of the method is proved in weighted spaces with uniform norm. Moreover, an error estimate of the numerical solution is given under certain assumptions on the Mellin kernel. The efficiency of the method is shown through some examples. The numerical results also confirm that the error estimate is sharp.
A new stable numerical method for Mellin integral equations in weighted spaces with uniform norm
Concetta Laurita
2020-01-01
Abstract
In this paper a new modified Nyström method is proposed to solve linear integral equations of the second kind with fixed singularities of Mellin convolution type. It is based on the Gauss-Radau quadrature formula with a suitable Jacobi weight. The stability and convergence of the method is proved in weighted spaces with uniform norm. Moreover, an error estimate of the numerical solution is given under certain assumptions on the Mellin kernel. The efficiency of the method is shown through some examples. The numerical results also confirm that the error estimate is sharp.File in questo prodotto:
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