BIT

We investigate full rank interpolatory vector subdivision schemes whose masks are positive definite on the unit circle except the point z=1. Such masks are known to give rise to convergent schemes with a cardinal limit function in the scalar case. ...

We show that the cost of solving initial value problems for high-index differential algebraic equations is polynomial in the number of digits of accuracy requested. The algorithm analyzed is built on a Taylor series method developed by Pryce for ...

It is shown that the Euler–Maruyama scheme applied to a stochastic differential equation with a discontinuous monotone drift coefficient, such as a Heaviside function, and additive noise converges strongly to a solution of the stochastic ...

Classical collocation RK methods are polynomially fitted in the sense that they integrate an ODE problem exactly if its solution is an algebraic polynomial up to some degree. Functionally fitted RK (FRK) methods are collocation techniques that ...

The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driving the development of a rich and detailed theory. Part of this theory is devoted to computer searches for rules, appropriate to particular ...

We characterize the boundary ∂Σ^p of the solution set Σ^p of a parametric linear system A(p)x=b(p) where the elements of the n×n matrix and the right-hand side vector depend on a number of parameters p varying within interval bounds. The ...

Consider a homogeneous parabolic problem on a smooth bounded domain in ℝ ^N but with initial data and Neumann boundary data of low regularity. Sharp interior maximum norm error estimates are given for a semidiscrete C ⁰ finite element approximation ...

As an application of the symmetric-triangular (ST) decomposition given by Golub and Yuan (2001) and Strang (2003), three block ST preconditioners are discussed here for saddle point problems. All three preconditioners transform saddle point ...