Solving Fredholm integral equations by approximating kernels by spline quasi-interpolants

Authors:
Chafik Allouch;Paul Sablonnière;Driss Sbibih
Affiliations:
Ecole Supérieure de Technologie, Laboratoire MATSI, Université Mohammed I, Oujda, Morocco;INSA de Rennes, Centre de Mathématiques, Rennes, France;Ecole Supérieure de Technologie, Laboratoire MATSI, Université Mohammed I, Oujda, Morocco
Venue:
Numerical Algorithms
Year:
2011

Citing 2
Cited 3

Integral equations: theory and numerical treatment

Integral equations: theory and numerical treatment
Numerical Computations, Volume II

Numerical Computations, Volume II

The numerical method of successive interpolations for Fredholm functional integral equations

Numerical Algorithms
About a numerical method of successive interpolations for functional Hammerstein integral equations

Journal of Computational and Applied Mathematics
Original article: Iteration methods for Fredholm integral equations of the second kind based on spline quasi-interpolants

Mathematics and Computers in Simulation

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Abstract

We study two methods for solving a univariate Fredholm integral equation of the second kind, based on (left and right) partial approximations of the kernel K by a discrete quartic spline quasi-interpolant. The principle of each method is to approximate the kernel with respect to one variable, the other remaining free. This leads to an approximation of K by a degenerate kernel. We give error estimates for smooth functions, and we show that the method based on the left (resp. right) approximation of the kernel has an approximation order O(h 5) (resp. O(h 6)). We also compare the obtained formulae with projection methods.