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- W1555544208 abstract "The Top Order Methods are a class of linear multistep schemes to be used as Boundary Value Methods and with the feature of having maximal order (2k if k is the number of steps). This often implies that accurate numerical approximations of general BVPs can be produced just using the 3‐step TOM. In this work, we consider two different possibilities for defining a continuous approximation of the numerical solution, the standard C1 cubic spline collocating the differential equation at the knots and a C2k−1 spline of degree 2k. The computation of the B‐spline coefficients of this higher degree spline requires the solution of N+2k banded linear systems of size 4k×4k. The resulting B‐spline function is convergent of order 2k to the exact solution of the continuous BVPs." @default.
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- W1555544208 date "2007-01-01" @default.
- W1555544208 modified "2023-10-18" @default.
- W1555544208 title "High Order Continuous Approximation for the Top Order Methods" @default.
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- W1555544208 doi "https://doi.org/10.1063/1.2790221" @default.
- W1555544208 hasPublicationYear "2007" @default.
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