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首页> 外文期刊>Discrete and continuous dynamical systems▼hSeries S >SPECTRAL JACOBI-GALERKIN METHODS AND ITERATED METHODS FOR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND WITH WEAKLY SINGULAR KERNEL
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SPECTRAL JACOBI-GALERKIN METHODS AND ITERATED METHODS FOR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND WITH WEAKLY SINGULAR KERNEL

机译：光谱Jacobi-Galerkin方法和迭代方法，用于第二种与弱奇异内核的第二种弗雷霍姆积分方程

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摘要

We consider spectral and pseudo-spectral Jacobi-Galerkin meth-ods and corresponding iterated methods for Fredholm integral equations of the second kind with weakly singular kernel. The Gauss-Jacobi quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical im-plementation. We obtain the convergence rates for the approximated solution and iterated solution in weakly singular Fredholm integral equations, which show that the errors of the approximate solution decay exponentially in L∞-norm and weighted L~2-norm. The numerical examples are given to illustrate the theoretical results.
机译：我们考虑光谱和伪光谱Jacobi-Galerkin Meth-OD，以及用于第二种与弱奇异内核的第二类Fredholm整体方程的相应迭代方法。高斯-Jacobi正交配方用于近似于数值实施方式的基于Jacobi重量的整体算子和内部产品在数值电压的弱配方中实现。我们在弱奇异的Fredholm积分方程中获得了近似解和迭代解的收敛速率，这表明近似解衰减的误差呈符号为L∞ - 规范和加权L〜2-Norm。给出了数值例子来说明理论结果。

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