Iterated Petrov–Galerkin Method with Regular Pairs for Solving Fredholm Integral Equations of the Second Kind
Departamento de Matemática, Facultad de Ingeniería, Universidad de Buenos Aires, C1063ACV Buenos Aires, Argentina
Author to whom correspondence should be addressed.
Received: 22 October 2018 / Revised: 9 November 2018 / Accepted: 12 November 2018 / Published: 13 November 2018
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In this work we obtain approximate solutions for Fredholm integral equations of the second kind by means of Petrov–Galerkin method, choosing “regular pairs” of subspaces,
which are simply characterized by the positive definitiveness of a correlation matrix. This choice guarantees the solvability and numerical stability of the approximation scheme in an easy way, and the selection of orthogonal basis for the subspaces make the calculations quite simple. Afterwards, we explore an interesting phenomenon called “superconvergence”, observed in the 1970s by Sloan: once the approximations
to the solution of the operator equation
are obtained, the convergence can be notably improved by means of an iteration of the method,
. We illustrate both procedures of approximation by means of two numerical examples: one for a continuous kernel, and the other for a weakly singular one.
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Seminara, S.A.; Troparevsky, M.I. Iterated Petrov–Galerkin Method with Regular Pairs for Solving Fredholm Integral Equations of the Second Kind. Math. Comput. Appl. 2018, 23, 73.
Seminara SA, Troparevsky MI. Iterated Petrov–Galerkin Method with Regular Pairs for Solving Fredholm Integral Equations of the Second Kind. Mathematical and Computational Applications. 2018; 23(4):73.
Seminara, Silvia A.; Troparevsky, María I. 2018. "Iterated Petrov–Galerkin Method with Regular Pairs for Solving Fredholm Integral Equations of the Second Kind." Math. Comput. Appl. 23, no. 4: 73.
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