A higher order Faber spline basis for sampling discretization of functions

An ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems

As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...

Higher-order compatible discretization on hexahedrals

We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the vorticityvelocity-pressure formulation of the Stokes problem. We motivate the choice for a mixed variational formulation based on both geometric as well as physical arguments...

Deforestation for Higher-Order Functions

Higher Order Functions Considered Unnecessary for Higher Order Programming

It is often claimed that the essence of functional programming is the use of functions as values, i.e., of higher order functions, and many interesting examples have been given showing the power of this approach. Unfortunately, the logic of higher order functions is diicult, and in particular, higher order uniication is undecidable. Moreover (and closely related), higher order expressions are n...

Higher-Order Functions for Parsing

In combinator parsing , the text of parsers resembles BNF notation. We present the basic method, and a number of extensions. We address the special problems presented by white– space, and parsers with separate lexical and syntactic phases. In particular, a combining form for handling the “offside rule” is given. Other extensions to the basic method include an “into” combining form with many use...