## Extensions of the Nyström Method for the Numerical Solution of Linear Integral Equations of the Second KindNumerical methods are presented for the solution of various problems associated with Fredholm linear integral equations of the second kind. (Author). |

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### Contents

An Extension of the Nystrom Method to Kernels with | 24 |

Integral Equations of the Second Kind Which Are | 49 |

The Numerical Solution of the Eigenvalue Problem | 66 |

1 other sections not shown

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Anselone apply Theorem arbitrary Arzela-Ascoli Theorem assumed assumptions Banach space bounded linear operator boundedness calculation chapter compact closure compact operator computation define denote E(cr eigenfunctions eigenvalue problem eigenvectors equal finite dimension equation 1.1 equicontinuous error analysis error bounds error estimates error formula Error Ratio exists f(tMt)dt finite rank following theorem Fredholm Alternative functional analysis Gaussian quadrature given hypotheses B1-B3 implies inequality Integralgleichungen Kantorovich and Krylov Lemma Let f linear independence LINEAR INTEGRAL EQUATIONS llx-x llxll Math maximum Mysovskih necessary Null numerical solution Nystrom method order of convergence Peano Proof quadrature error quadrature points quadrature rules quantities rectangular rule respect right-hand side second kind sequence Simpson's rule solution of integral split sub-intervals subspace Theorem 1.1 theory thesis trapezoidal rule trivial true answer uniform bound uniform norm uniformly uniquely solvable University of Wisconsin usual Wielandt X-to Xx(s zero