Mixed Monotone Iterative Technique and Boundary Value Problem for a Class of Impulsive Integro-Differential Equations

In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.

Mixed Monotone Iterative Technique for Singular Hadamard Fractional Integro-Differential Equations in Banach Spaces

This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.

MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.

Monotone Iterative Method for Nonlinear Discontinuous Differential Equations

A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalization of the classical monotone iteration theory for continuous problems.

ON MONOTONE ITERATIVE METHOD FOR INITIAL VALUE PROBLEMS OF NONLINEAR SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.

SOME NEW ITERATIVE ALGORITHMS FOR MONOTONE MIXED VARIATIONAL INEQUALITIES

In this paper,some new iterative algorithms for monotone mixed variational inequalities and the convergence in real Hilbert spaces are studied.

Monotone Iterative Methodfor Nonlinear Discontinuous ParabolicDifferential Equations

In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.

Passive seismic velocity tomography on longwall mining panel based on simultaneous iterative reconstructive technique (SIRT)

Mining operation, especially underground coal mining, always has the remarkable risks of ground control. Passive seismic velocity tomography based on simultaneous iterative reconstructive technique （SIRT） inversion is used to deduce the stress redistribution around the longwall mining panel. The mining-induced microseismic events were recorded by mounting an array of receivers on the surface, above the active panel. After processing and filtering the seismic data, the three-dimensional tomography images of the p-wave velocity variations by SIRT passive seismic velocity tomography were provided. To display the velocity changes on coal seam level and subsequently to infer the stress redistribution, these three-dimensional tomograms into the coal seam level were sliced. In addition, the boundary element method （BEM） was used to simulate the stress redistribution. The results show that the inferred stresses from the passive seismic tomograms are conformed to numerical models and theoretical concept of the stress redistribution around the longwall panel. In velocity tomograms, the main zones of the stress redistribution arotmd the panel, including front and side abutment pressures, and gob stress are obvious and also the movement of stress zones along the face advancement is evident. Moreover, the effect of the advance rate of the face on the stress redistribution is demonstrated in tomography images. The research result proves that the SIRT passive seismic velocity tomography has an ultimate potential for monitoring the changes of stress redistribution around the longwall mining panel continuously and subsequently to improve safety of mining operations.

Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an iterative method based on the modified Vlasov model. On the basisof the principle of minimum potential energy, the governing differential equations and boundaryconditions for circular thin plates on modified Vlasov foundation considering the characteristics ofGibson soil are derived. The equations for the attenuation parameter in bending problem are alsoobtained, and the issue of unknown parameters being difficult to determine is solved using theiterative method. Numerical examples are analyzed and the results are in good agreement withthose form other literatures. It proves that the method is practical and accurate. Theinhomogeneity of modified Vlasov foundations has some influence on the deformation andinternal force behavior of circular thin plates. The effects of various parameters on the bending ofcircular plates and characteristic parameters of the foundation are discussed. The modified modelfurther enriches and develops the elastic foundations. Relevant conclusions that are meaningful toengineering practice are drawn.

AN ITERATIVE ALGORITHM FOR MAXIMAL MONOTONE MULTIVALUED OPERATOR EQUATIONS

A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.

The Iterative Solution for a Class of Monotone Operator Equations

The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented, An iterative algorithm for approximating the solutions of generalized implicit wriational- like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved,

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].

ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.

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.

New Fourth and Fifth-Order Iterative Methods for Solving Nonlinear Equations

In this paper, we establish two new iterative methods of order four and five by using modified homotopy perturbation technique. We also present the convergence analysis of these iterative methods. To assess the validity and performance of these iterative methods, we have applied to solve some nonlinear problems.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.