| We mainly examine the application of the improved version of the quasi-minimal residual (IQMR) method 20], 21] for the solutions of linear systems of equations with unsymmetric coeecient matrices arising from the discretization of uid dynamic problems on massively parallel distributed memory computers. We will deal with implicit nite diierence schemes for solving the Euler equations. These sc...

For an implicit multifunction (p) defined by the generally nonsmooth equation F(x, p) = 0, contingent derivative formulas are derived, being similar to the formula ′ = −Fx−1Fp in the standard implicit function theorem for smooth F and . This will be applied to the projection X(p) = {x | ∃y: (x, y) ∈ (p)} of the solution set (p) of the system F(x, y, p) = 0 onto the x-space. In particular settin...

In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtaine...

Implicit extrapolation is an efficient and unconditionally stable method of wavefield continuation. Unfortunately, implicit wave extrapolation in three dimensions requires an expensive solution of a large system of linear equations. However, by mapping the computational domain into one dimension via the helix transform, we show that the matrix inversion problem can be recast in terms of an effi...

A type of coupled map lattice (CML) is considered in this paper. What we want to do is to define the form of a traveling wave solution and to reveal its existence. Due to the infinite property of the problem, we have tried the periodic case, which can be dealt with on a finite set. The main approach for our study is the implicit existence theorem. The results indicate that if the parameters of ...

We derive a deterministic particle method for the solution of nonlinear reactiondiffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of ...

Implicit extrapolation is an eecient and unconditionally stable method of wave-eld continuation. Unfortunately, implicit wave extrapolation in three dimensions requires an expensive solution of a large system of linear equations. However, by mapping the computational domain into one dimension via the helix transform, we show that the matrix inversion problem can be recast in terms of an eecient...

We introduce a general implicit algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the solution...