B-Spline Linear Multistep Methods and their Continuous Extensions
SIAM Journal on Numerical Analysis
The continuous extension of the B-spline linear multistep methods for BVPs on non-uniform meshes
Applied Numerical Mathematics
Applied Numerical Mathematics
Block boundary value methods for solving Volterra integral and integro-differential equations
Journal of Computational and Applied Mathematics
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Two new classes of quadrature formulas associated to the BS Boundary Value Methods are discussed. The first is of Lagrange type and is obtained by directly applying the BS methods to the integration problem formulated as a (special) Cauchy problem. The second descends from the related BS Hermite quasi-interpolation approach which produces a spline approximant from Hermite data assigned on meshes with general distributions. The second class formulas is also combined with suitable finite difference approximations of the necessary derivative values in order to define corresponding Lagrange type formulas with the same accuracy.