Convergence analysis and parity conservation of a new form of a quadratic explicit spline with applications to integral equations

In this study, a new form of a quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve integral equations.Fil: Ferrari, Alberto José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Lara, Luis Pedro. Universidad del Centro Educativo Latinoamericano; ArgentinaFil: Santillan Marcus, Eduardo Adrian. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

Discrete biquintic spline method for Fredholm integral equations of the second kind

To find approximate solutions of Fredholm integral equations, we degenerate the kernels by discrete biquintic splines. Explicit a priori and posteriori error bounds are derived and a numerical example is presented to confirm the theoretical results