Abstract In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote variational inequality problem, general system of inequalities, hierarchical inequality, common fixed-point problem countable family uniformly Lipschitzian pseudocontractive mappings an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-s...

In this paper, we present error corrected Euler methods for solving stiff initial value problems, which not only avoid unnecessary iteration process that may be required in most implicit methods but also have such a good stability as all implicit methods possess. The proposed methods use a Chebyshev collocation technique as well as an asymptotical linear ordinary differential equation of first-...

We develop an implicit discretization method for pricing European and American options when the underlying asset is driven by an infinite activity Lévy process. For processes of finite variation, quadratic convergence is obtained as the mesh and time step are refined. For infinite variation processes, better than first order accuracy is achieved. The jump component in the neighborhood of log ju...

The implicit equations of a symplectic-energymomentum integrator are not easily solved, especially for small time steps. An inefficient, nested iteration scheme has typically been used to solve these equations. We describe new, more efficient, iteration schemes which avoid nested iterations. We present simulation results comparing five different secondorder, integration methods for two differen...

The basic ideas of semi-implicit time differencing are reviewed, including analytical results not widely referenced in the meteorological literature. It is shown that solving the resulting implicit equations by simple fixed-point iteration requires a relatively small time step to guarantee convergence, thus defeating the purpose of the semiimplicit method. In contrast, classical iteration metho...

A self-consistent mean-field theory for bosons for T > 0 is used to reconcile predictions of collapse with recent observations of Bose-Einstein condensation of Li. Eigenfunctions of a (non-separable) Hamiltonian that includes the anisotropic external trap field and atom-atom interactions are obtained by an iteration process. A sum over the Bose distribution, and the “alternating direction impli...

The paper gives the numerical stencil for the two-dimensional convection diffusion equation and the technique of elimination, and builds up the new iterative scheme to solve the implicit difference equation. The scheme’s convergence and its higher rate of convergence than the Jacobi iteration are proved. And the numerical example indicates that the new scheme has the same parallelism and a high...

American put options written on an underlying stock following a Carr-Madan-Geman-Yor (CGMY) process are considered. It is known that American option prices satisfy a Partial Integro-Differential Equation (PIDE) on a moving domain. These equations are reformulated as a Linear Complementarity Problem, and solved iteratively by an implicit-explicit type of iteration based on a convenient splitting...