Recently two kinds of HSS-based iteration methods to solve the absolute value equation (AVE) are proposed. In present paper, we focus on developing the CSCSbased methods for solving the absolute value equation (AVE) involving the Toeplitz structure, and propose the Picard-CSCS method and the nonlinear CSCS-like iterative method. With the help of introducing a smoothing approximate function, we ...

Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to sequence functions and modify norm in its internal optimization problem H−s norm, some positive integer s, bias it towards low-frequency spectral content residual. We analyze by quantifying improvement over Picard iteration. find that based on H−2 well-suited solve...

We study the pointwise behavior of the linearized Boltzmann equation on torus for non-smooth initial perturbations. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier modes for the space variable, and the time decay rate of the fluid-like waves depends on the size of the doma...

In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension n in terms of differential forms. In the case n = 1 such computations have many applications in differential equations and counting their limit cycles. For n > 3, these computations give us an explicit...

We present and analyze an algorithm to solve numerically BSDEs based on Picard’s iterations and on a sequential control variate technique. Its convergence is geometric. Moreover, the solution provided by our algorithm is regular both w.r.t. time and space.

*Correspondence: [email protected] College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, P.R. China Abstract Choosing space Cg as the phase space, the existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay (short for INSFDEs) are studied in this paper. Under non-Lipschitz condition, weakened ...

A higher-order Godunov method for the radiation subsystem of radiation hydro-dynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation laws; it is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The method is second-o...

Recently, Samet et al [24] introduced the concept of α-ψ contractive mappings and studied the existence of fixed points for such mappings. In this article, we prove three fixed point theorems for this class of operators in complete metric spaces. Our results extend the results in [24] and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ćirić, Niet...