SIAM Journal on Numerical Analysis

For a scalar conservation law $u_t = f(u)_x $ with $f''$ of constant sign, the first order upwind difference scheme is a special case of Godunov’s method. The method is equivalent to solving a sequence of Riemann problems at each step and averaging the ...

In the present paper we are concerned with the approximation of cosine operator functions which appear in a natural way in the study of the Cauchy problem for second order evolution equations. We derive both qualitative and quantitative convergence ...

In this paper the implicit time discretization of $E_t - \nabla \cdot K\nabla T = f$, the enthalpy formulation of the Stef an problem, is considered. This generates the algebraic system $E + A\beta (E) = \eta $, where E, $\beta (E)$, $\eta \in {}^ + \...

We give an algorithm for approximating the solution of the Stefan problem. This problem may have thermal properties and forcing terms that depend on the space variable, temperature or temperature gradients. The resulting nonlinear algebraic problem has ...

Direct iterative methods for solving the linear system $AX = Y$ split A into a difference $M - N$. By viewing N as a weak multiplication operator, we determine the convergence rates of block direct iterative methods for elliptic and parabolic difference ...

We approximate a periodic linear parabolic problem using a Galerkin method for the space variable and a spectral method for the time variable. Some optimal error estimates are derived.

A finite element discretization of the criticality eigenvalue problem for a one-dimensional model of the transport equation is analyzed. The existence of spurious eigenvalues for this procedure is demonstrated. However, it is shown that all of the ...

Recently the present author has developed some high-order finite difference formulae for the approximate numerical integration of general two-point boundary value problems for ordinary differential equations. The algebraic equations arising from using ...

A new algorithm for solving finite element problems is presented. It blends a preconditioned conjugate gradient iteration into a direct factorization method. The goal was to reduce fill to a negligible level and thus reduce storage requirements, but the ...

An algorithm for computing a few of the smallest (or largest) eigenvalues and associated eigenvectors of the large sparse generalized eigenvalue problem $Ax = \lambda Bx$ is presented. The matrices A and B are assumed to be symmetric, and haphazardly ...

A simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex.

The rate of convergence of line search algorithms based on general interpolating functions is derived and is shown to be independent of the particular interpolating function used. This result holds for the root finding problem $f(x) = 0$ as well. We show ...

We obtain Jackson type estimates for the approximation of increasing or convex functions by splines with the same property. These estimates are new when the knots are not uniformly spaced. The method of proof motivates an algorithm for fitting a curve to ...

An efficient computational method is presented for fitting a bivariate spline function to a set of measured data on a rectangular grid. The coefficients in the B-spline representation of this spline are obtained by the solution of a linear system which ...