Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation

This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.

MULTIRATE TIME ITERATIVE SCHEME WITH MULTIPHYSICS FINITE ELEMENT METHOD FOR A NONLINEAR POROELASTICITY

In this paper,a multirate time iterative scheme with multiphysics finite element method is proposed and analyzed for the nonlinear poroelasticity model.The original problem is reformulated into a generalized nonlinear Stokes problem coupled with a diffusion problem of a pseudo pressure field by a new multiphysics approach.A multiphysics finite element method is adopted for the spatial discretization,and the generalized nonlinear Stokes problem is solved in a coarse time step and the diffusion problem is solved in a finer time step.The proposed algorithm is a decoupled algorithm,which is easily implemented in computation and reduces greatly computation cost.The stability analysis and the convergence analysis for the multirate iterative scheme with multiphysics finite element method are given.Some numerical tests are shown to demonstrate and validate the analysis results.

General Synthetic Iterative Scheme for Unsteady Rarefied Gas Flows

In rarefied gas flows,the spatial grid size could vary by several orders of magnitude in a single flow configuration(e.g.,inside the Knudsen layer it is at the order of mean free path of gas molecules,while in the bulk region it is at a much larger hydrodynamic scale).Therefore,efficient implicit numerical method is urgently needed for time-dependent problems.However,the integro-differential nature of gas kinetic equations poses a grand challenge,as the gain part of the collision operator is non-invertible.Hence an iterative solver is required in each time step,which usually takes a lot of iterations in the(near)continuum flow regime where the Knudsen number is small;worse still,the solution does not asymptotically preserve the fluid dynamic limit when the spatial cell size is not refined enough.Based on the general synthetic iteration scheme for steady-state solution of the Boltzmann equation,we propose two numerical schemes to push the multiscale simulation of unsteady rarefied gas flows to a new boundary,that is,the numerical solution not only converges within dozens of iterations in each time step,but also asymptotically preserves the Navier-Stokes-Fourier limit in the continuum flow regime,when the spatial grid is coarse,and the time step is large(e.g.,in simulating the extreme slow decay of two-dimensional Taylor vortex,the time step is even at the order of vortex decay time).The properties of fast convergence and asymptotic preserving of the proposed schemes are not only rigorously proven by the Fourier stability analysis for simplified gas kinetic models,but also demonstrated by several numerical examples for the gas kinetic models and the Boltzmann equation.

An integer programming formulation and iterative scheme algorithm for the block relocation problem

In this paper, we deal with the unrestricted block relocation problem. We present a new integerprogramming formulation for solving the problem. The initial formulation is improved by tighteningconstraints and a pre-processing step to fix several variables. We design a exact iterativescheme algorithm based on a fast heuristic for the integer programming formulation (ISA-FH).Computational results show the effectiveness of the improved formulation and algorithm.

Combined iterative cross-correlation demodulation scheme for mixing space borne automatic identification system signals

Aiming at the potential presence of mixing automatic identification system(AIS) signals,a new demodulation scheme was proposed for separating other interfering signals in satellite systems.The combined iterative cross-correlation demodulation scheme,referred to as CICCD,yielded a set of single short signals based on the prior information of AIS,after the frequency,code rate and modulation index were estimated.It demodulates the corresponding short codes according to the maximum peak of cross-correlation,which is simple and easy to implement.Numerical simulations show that the bit error rate of proposed algorithm improves by about 40% compared with existing ones,and about 3 dB beyond the standard AIS receiver.In addition,the proposed demodulation scheme shows the satisfying performance and engineering value in mixing AIS environment and can also perform well in low signal-to-noise conditions.

Almost sure T-stability and convergence for random iterative algorithms

The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.

An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.

ITERATIVE ALGORITHMS FOR FINDING APPROXIMATE SOLUTIONS OF COMPLETELY GENERALIZED STRONGLY NONLINEAR QUASIVARIATIONAL INEQUALITIES

In this paper, we study, iterative algorithms.for finding approximate solutions ofcompletely generalized strongly nonlinear quasivariational inequalities which include,as a special case, some known results in this .field. Our results are the extension andimprovents of the results of Siddiqi and Ansari, Ding. and Zeng.

A New Multidimensional Time Series Forecasting Method Based on the EOF Iteration Scheme

In this paper a new .mnultidimensional time series forecasting scheme based on the empirical orthogonal function (EOF) stepwise iteration process is introduced. The scheme is tested in a series of forecast experiments of Nino3 SST anomalies and Tahiti-Darwin SO index. The results show that the scheme is feasible and ENSO predictable.

Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings

In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.

Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.

TRANSONIC FLOW CALCULATION OF EULER EQUATIONS BY IMPLICIT ITERATING SCHEME WITH FLUX SPLITTING

Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

Strong Convergence and Certain Control Conditions for Modified Ishikawa Type Iteration

In this paper, we establish the strong convergent theorems of an iterative algorithm for asymptotically nonexpansive mappings in Banach spaces and nonexpansive mappings in uniformly smooth Banach spaces, respectively. The results presented in this paper not only give an affirmative partial answer to Reich's open question, but also generalize and improve the corresponding results of Chang, Lee and Chan [7] and Kim and Xu [10] .

Multigrid Methods for Time-Fractional Evolution Equations:A Numerical Study

In this work,we develop an efficient iterative scheme for a class of nonlocal evolution models involving a Caputo fractional derivative of orderα(0,1)in time.The fully discrete scheme is obtained using the standard Galerkin method with conforming piecewise linear finite elements in space and corrected high-order BDF convolution quadrature in time.At each time step,instead of solving the linear algebraic system exactly,we employ a multigrid iteration with a Gauss–Seidel smoother to approximate the solution efficiently.Illustrative numerical results for nonsmooth problem data are presented to demonstrate the approach.

Fixed Point Approximation for Suzuki Generalized Nonexpansive Mapping Using B(δ, μ) Condition

In this paper, we introduce AK' iteration scheme to approximate fixed point for Suzuki generalized nonexpansive mapping satisfying B(δ, μ) condition in the framework of Banach spaces. Also, an example is given to confirm the efficiency of AK' iteration scheme. Our results are generalizations in the existing literature of fixed points in Banach spaces.

A Mixed Real-time Algorithm for the Forward Kinematics of Stewart Parallel Manipulator

Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Firstly taking advantage of simpleness of inverse kinematics, the forward kinematics is transformed to an optimal problem. Immune evolutionary algorithm is employed to find approximate solution of this optimal problem in manipulator＇s workspace. Then using above solution as iterative initialization, a speedy numerical iterative scheme is proposed to get more precise solution. In the manipulator running course, the iteration initialization can be selected as the last period position and orientation. Because the initialization is closed to correct solution, solving precision is high and speed is rapid enough to satisfy real-time requirement. This mixed forward kinematics algorithm is applied to real Stewart parallel manipulator in the real-time control course. The examination result shows that the algorithm is very efficient and practical.

Numerical investigations to design a novel model based on the fifth order system of Emden–Fowler equations

The aim of the present study is to design a new fifth order system of Emden–Fowler equations and related four types of the model.The standard second order form of the Emden–Fowler has been used to obtain the new model.The shape factor that appear more than one time discussed in detail for every case of the designed model.The singularity atη=0 at one point or multiple points is also discussed at each type of the model.For validation and correctness of the new designed model,one example of each type based on system of fifth order Emden–Fowler equations are provided and numerical solutions of the designed equations of each type have been obtained by using variational iteration scheme.The comparison of the exact results and present numerical outcomes for solving one problem of each type is presented to check the accuracy of the designed model.

Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Ф-pseudocontractive Mappings

Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.