Extrapolation of a discrete collocation-type method of Hammerstein equations

AbstractIn recent papers, Kumar and Sloan introduced a new collocation-type method for numerical solution of Hammerstein integral equations. Kumar studied a discretized version of this method and obtained superconvergence rate for the discrete approximation to the exact solution. In this paper, the asymptotic error expansion of a discrete collocation-type method for Hammerstein integral equations is obtained. We show that when piecewise polynomials of degree p − 1 are used and numerical quadrature is used to approximate the definite integrals occurring in this method, the approximation solution admits an error expansion in powers of the step-size h. For a special choice of collocation points and numerical quadrature rule, the leading terms in the error expansion for the collocation solution contain only even powers of the step-size h, beginning with a term h2p. Thus Richardson's extrapolation can be performed on the solution, and this will increase the accuracy of numerical solution greatly. Some numerical results are given to illustrate this theory

Proceedings of the 1968 Summer Institute on Symbolic Mathematical Computation

Investigating symbolic mathematical computation using PL/1 FORMAC batch system and Scope FORMAC interactive syste

SPECTRAL METHODS FOR HYPERBOLIC PROBLEMS

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