The Richards equation is widely used in the simulation of unsaturated flow and related fields. In numerical solution process, finite volume method can be to carry out discretization, Picard for iterative solution. However, order obtain a more reliable solution, space step size conventional uniform grid often small. Especially under some unfavorable conditions, such as infiltration into dry soil...

In this work, we present a two-dimensional mixed-hybrid finite element model of variably saturated flow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations in combination with ad hoc preconditioning tech...

The purpose of this paper is to introduce a new class of quasi-contractive operators and to show that the most used fixed point iterative methods, that is, the Picard and Mann iterations, are convergent to the unique fixed point. The comparison of these methods with respect to their convergence rate is obtained.

In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method  and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. F...

In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using Picard iteration method. The paper provides new results integral calculus techniques. We have shown convergence solution averaged PIDSFOS to that standard in context mean square also probability. One example is given illustrate our results.

Let {Xn} be a sequence of i.i.d. random vectors with values in a separable Banach space. Moderate deviation principles for trajectories of sums of {Xn} are proved, which generalize related results of Borovkov and Mogulskii (1980) and Deshayes and Picard (1979). As an application, functional laws of the iterated logarithm are given. The paper also contains concluding remarks, with examples, on e...