We introduce and study a new class of generalized nonlinear implicit quasivariational inclusions involving relaxed Lipschitzian mappings. We prove the existence of solution for the generalized nonlinear implicit quasivariational inclusions and construct some new stable perturbed iterative algorithms with errors. We also give an application to a class of generalized nonlinear implicit variationa...

In this paper we establish the stability condition of a general class of finite difference schemes applied to nonlinear complex reaction-diffusion equations. We consider the numerical solution of both implicit and semi-implicit discretizations. To illustrate the theoretical results we present some numerical examples computed with a semi-implicit scheme applied to a nonlinear equation.

This paper investigates the expected benefits of the implicit time integration scheme in the solution of jointed rock problems. Discontinuous Deformation Analyses (DDA) exploits the unconditional stability of the implicit time integration scheme, and allows the time step size of the solution to be much larger than the critical time step size dictated by the stability requirement of the explicit...

Randomized linear system solvers have become popular as they the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising cla...