‎In this paper we propose a new iteration process‎, ‎called the $K^{ast }$ iteration process‎, ‎for approximation of fixed‎ ‎points‎. ‎We show that our iteration process is faster than the existing well-known iteration processes using numerical examples‎. ‎Stability of the $K^{ast‎}‎$ iteration process is also discussed‎. ‎Finally we prove some weak and strong convergence theorems for Suzuki ge...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach...

Abstract We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time investigate the influence iterative methods used to solve arising equations. show that Newton’s method can turn an scheme into anti-dissipative one, even when iteration error is smaller than integration error. explore several remedies, which most performant a relaxation te...

We analyze a number of techniques for pricing American options under a regime 4 switching stochastic process. The techniques analyzed include both explicit and implicit discretiza5 tions with the focus being on methods which are unconditionally stable. In the case of implicit 6 methods we also compare a number of iterative procedures for solving the associated nonlinear al7 gebraic equations. N...