Convergence analysis of discrete legendre spectral projection methods for hammerstein integral equations of mixed type

Das, Payel; Nelakanti, Gnaneshwar

doi:10.1016/j.amc.2015.05.100

Cited by 10 publications

(3 citation statements)

References 26 publications

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“…To solve the various integral equations and the eigenvalue problem, numerically spectral projection methods have been used by various researchers (see, [1][2][3][4][5][6]). Legendre spectral approximation method for eigenvalue problem of a compact integral operator is developed in [7].…”

Section: Introductionmentioning

confidence: 99%

Discrete Legendre Projection Methods for the Eigenvalue Problem of a Compact Integral Operator

Panigrahi¹,

Malik²

2016

JCSCM

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In this paper, we consider the discrete Legendre projection methods to solve the eigenvalue problem. Using sufficiently accurate numerical quadrature rule, we obtain the error bounds for gap between the spectral subspaces, eigenvalues and iterated eigenvectors for the eigenvalue problem in 2 L norm. We also obtain the superconvergence results for eigenvalues and iterated eigenvectors in discrete Legendre Galerkin methods. Numerical examples are presented to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Discrete Legendre Projection Methods for the Eigenvalue Problem of a Compact Integral Operator

Panigrahi¹,

Malik²

2016

JCSCM

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“…There has been a notable interest in the numerical analysis of solutions of intergal equations (see [1][2][3][4][5][6][7][8][9][10][11]). The Galerkin, collocation, Petrov-Galerkin, degenerate kernel and Nystrm methods are the most frequently used projection methods for solving the equations of type (1).…”

Section: Introductionmentioning

confidence: 99%

“…Hence in such cases, one has to solve a large system of nonlinear equations, which is computationally very much expensive. To overcome the computational complexities encountered in the existing piecewise polynomial based projection methods, we apply polynomially-based projection methods to nonlinear Fredholm integral equations ( [4,5,17,18]). We choose the approximating subspaces to be global polynomial subspaces of degree which has dimension + 1.…”

Section: Introductionmentioning

confidence: 99%