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math.CA2012
Optimal error estimates for corrected trapezoidal rules
Erik Talvila, Matthew Wiersma
Corrected trapezoidal rules are proved for under the assumption that for some . Such quadrature rules involve the trapezoi…
math.CA2012★ 5 cited
Simple derivation of basic quadrature formulas
Erik Talvila, Matthew Wiersma
Simple proofs of the midpoint, trapezoidal and Simpson's rules are proved for numerical integration on a compact interval. The integrand is assumed to be twice continuously differe…
math.CA2011★ 2 cited
Quadrature rules with (not too many) derivatives
Matthew Wiersma
Quadrature formulas for where derivative terms need only be evaluated at and in the composite rule are identified. Error bounds are given when $f:[a,b]\t…