International Journal of Computer Mathematics ( IF 1.8 ) Pub Date : 2021-03-02 , DOI: 10.1080/00207160.2021.1891225 Moumita Mandal 1 , Kapil Kant 2 , Gnaneshwar Nelakanti 2
In this article, we study the discrete version of Legendre spectral and iterated Legendre spectral techniques to solve the second kind Hammerstein type weakly singular integral equations. To obtain the convergence analysis, we use the appropriate numerical quadrature rule and obtain the order in discrete Legendre spectral method. If the quadrature rule is minimal, i.e. the number of quadrature nodes and the dimension of the approximating subspace are same, then the optimal rate is obtained in iterated form of discrete Legendre spectral collocation method in norm and uniform norm. Numerical aspects are given to verify the hypothetical results.
中文翻译:
Hammerstein型弱奇异非线性Fredholm积分方程的离散Legendre谱方法
在本文中,我们研究离散版本的勒让德谱和迭代勒让德谱技术来求解第二类 Hammerstein 型弱奇异积分方程。为了获得收敛分析,我们使用适当的数值求积规则并获得阶数在离散勒让德谱方法中。如果正交规则最小,即正交节点数和逼近子空间的维数相同,则得到最优速率 离散Legendre谱搭配方法的迭代形式 范数和统一范数。给出了数值方面来验证假设结果。