van der Houwen, P.J. Messina, E.
Published in
Numerical Algorithms

We consider implicit integration methods for the solution of stiff initial value problems for second-order differential equations of the special form y'' = f(y). In implicit methods, we are faced with the problem of solving systems of implicit relations. This paper focuses on the construction and analysis of iterative solution methods which are eff...

Ariyawansa, K.A.
Published in
Numerical Algorithms

Collinear scaling algorithms related to direct fixed-scale and rescaled least-change secant update methods for unconstrained minimization are derived. Theorems on local and q-superlinear convergence of these algorithms are presented. These results are extensions of those of Dennis and Walker [14] for direct least-change secant update methods.

Espedal, Magne S. Tai, Xue‐Cheng Yan, Ningning
Published in
Numerical Algorithms

Two nonoverlapping domain decomposition algorithms are proposed for convection dominated convection–diffusion problems. In each subdomain, artificial boundary conditions are used on the inflow and outflow boundaries. If the flow is simple, each subdomain problem only needs to be solved once. If there are closed streamlines, an iterative algorithm i...

Stynes, Martin Tobiska, Lutz
Published in
Numerical Algorithms

We consider streamline diffusion finite element methods applied to a singularly perturbed convection–diffusion two‐point boundary value problem whose solution has a single boundary layer. To analyse the convergence of these methods, we rewrite them as finite difference schemes. We first consider arbitrary meshes, then, in analysing the scheme on a ...

Essai, Azeddine
Published in
Numerical Algorithms

This paper presents two new methods called WFOM and WGMRES, which are variants of FOM and GMRES, for solving large and sparse nonsymmetric linear systems. To accelerate the convergence, these new methods use a different inner product instead of the Euclidean one. Furthermore, at each restart, a different inner product is chosen. The weighted Arnold...

Segura, Javier
Published in
Numerical Algorithms

The zeros of cylinder functions Cu(x)=cos α, Ju(x) - sin α, Yu(x) coincide with those of the ratios Hu(x)=Cu(x)/Cu-1(x) except, perhaps, at x = 0. We show monotonicity properties of Hu(x) and fu(x) = x2v-1Hu(x) and their derivatives for x > 0. We then build a Newton-Raphson iterative method based on the monotonic function fu(x) which is shown to be...

Bar‐On, Ilan Leoncini, Mauro
Published in
Numerical Algorithms

In this paper we present three different pivoting strategies for solving general tridiagonal systems of linear equations. The first strategy resembles the classical method of Gaussian elimination with no pivoting and is stable provided a simple and easily checkable condition is met. In the second strategy, the growth of the elements is monitored so...

Piquet, Jean Vasseur, Xavier
Published in
Numerical Algorithms

We consider numerical methods for the incompressible Reynolds averaged Navier–Stokes equations discretized by finite difference techniques on non-staggered grids in body-fitted coordinates. A segregated approach is used to solve the pressure–velocity coupling problem. Several iterative pressure linear solvers including Krylov subspace and multigrid...

Chan, Tony F. de Pillis, Lisette van der Vorst, Henk
Published in
Numerical Algorithms

We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix–vector products per iteration without accessing AT. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal [15] (with...

Butcher, J.C. Diamantakis, M.T.
Published in
Numerical Algorithms

To overcome known disadvantages in the use of singly-implicit methods in the solution of stiff differential equations, two generalizations have been recently introduced. These are the use of additional diagonally-implicit stages and the use of effective order as a weakening of the conditions on the method. In this paper, these two generalizations a...