Asymptotic error expansion of a c error expansion of a colloation-type method for Hammerstein equations
The authors obtain an asymptotic error expansion of a collocation-type method for Hammerstein equations of the form \[ y(x) = f(x) + \int^b_a K(x,t) g(t,y(t))dt, \quad a \leq x \leq b, \] [see also \textit{S. Kumar} and \textit{I. H. Sloan}, Math. Comput. 48, 585-593 (1987; Zbl 0616.65142)]. They demonstrate that the approximate solution to \(y(x)\) admits an error expansion in even powers of the step-size \(h\), beginning with a term \(h^{2p}\), using piecewise polynomials of \(\Pi_{p-1}\). Thus Richardson's extrapolation can be performed on the solution and the accuracy of the numerical solution is greatly increased.
scientific article; zbMATH DE number 803671