Asymptotic error expansions for defect correction iterates

The structure of the global discretization error is studied for the implicit midpoint and trapezoidal rules applied to nonlinear stiff initial value problems. The point is that, in general, the global error contains nonsmooth (oscillating) terms at ...

This paper presents quadrature formulae for hypersingular integrals $\int_a^b\frac{g(x)}{|x-t|^{1+\alpha }}\mathrm{d}x$ , where a < t < b and 0 < 1. The asymptotic error estimates obtained by Euler---Maclaurin expansions show that, if g ( x ) is 2 m times differentiable on [ a , b ], the ...

The existence of asymptotic expansions of the global discretization error for a general class of nonlinear stiff differential equations \[ y'(t) = A(t)y(t) + \varphi (t,y(t)), \] where $A(t)$ has a “stiff spectrum” characterized by a small parameter $\...