In this article, we present generalized conditions of three-step iterative schemes for solving nonlinear equations. The convergence order is shown using Taylor series, but the existence high-order derivatives assumed. However, only first derivative appears on these schemes. Therefore, hypotheses limit utilization to operators that are at least nine times differentiable, although may converge. T...

Abstract In the article a convergent numerical method for conservative solutions of Hunter–Saxton equation is derived. The based on piecewise linear projections, followed by evolution along characteristics where time step chosen in order to prevent wave breaking. Convergence obtained when proportional square root spatial size, which milder restriction than common CFL condition conservation laws.

Given nite subset J IR n , and a point 2 IR n , we study in this paper the possible convergence, as h ! 0, of the coeecients in least-squares approximation to f(+hh) from the space spanned by (f(+ hj) j2J. We invoke thèleast solution of the polynomial interpolation problem' to show that the coeecient do converge for a generic J and , provided that the underlying function f is suuciently smooth....