Non-uniform UE-spline quasi-interpolants and their application to the numerical solution of integral equations
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Universidad de Granada
Materia
UE-splines Marsden’s identity Quasi-interpolation Error estimate Numerical integration Numerical integration Fredholm integral equation Hammerstein integral equation
Date
2023-05-18Referencia bibliográfica
M.-Y.Nour,A.Lamnii,A.Zidnaetal. Non-uniform UE-spline quasi-interpolants and their application to the numerical solution of integral equations. Applied NumericalMathematics191(2023)29–44[https://doi.org/10.1016/j.apnum.2023.05.006]
Sponsorship
Universidad de Granada / CBUAAbstract
A construction of Marsden’s identity for UE-splines is developed and a complete proof is given. With the help of this identity, a new non-uniform quasi-interpolant that repro-duces the spaces of polynomial, trigonometric and hyperbolic functions are defined. Effi-cient quadrature rules based on integrating these quasi-interpolation schemes are derived and analyzed. Then, a quadrature formula associated with non-uniform quasi-interpolation along with Nyström’s method is used to numericallysolve Hammerstein and Fredholm integral equations. Numerical results that illustrate the effectiveness of these rules are pre-sented.
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