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This paper presents a new trigonometric composite Hermite interpolation method for solving Fredholm linear integral equations. This operator approximates locally both the function and its derivative, which is known on the subdivision nodes. Then we derive a class of quadrature rules with endpoint corrections based on integrating the composite Hermite interpolant. We also provide error estimation and numerical examples to illustrate that this new operator can provide highly accurate results.

Trigonometric Hermite interpolation method for Fredholm linear integral equations