Iterative Solution for Systems of Nonlinear Two Binary Operator Equations

Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are improved and generalized.

Revised Iterative Solution of Ground State of Double-Well Potential

The revised new iterative method for solving the ground state of Schroedingerequation is deduced. Based on Green functions defined by quadratures along a single trajectory thisiterative method is applied to solve the ground state of the double-well potential. The result iscompared to the one based on the original iterative method. The limitation of the asymptoticexpansion is also discussed.

Iterative Solution for Groundstate of H_2^+ Ion

To solve the wave functions and energies of the groundstate of H＋2 ion an iteration procedure for N- dimensional potentials is applied. The iterative solutions are convergent nicely, which are comparable to earlier results based on variational methods.

Iterative solutions for low lying excited states of a class of SchrSdinger equation

The convergent iterative procedure for solving the groundstate Schrodinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.

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.

ITERATIVE COMPUTATION METHOD FOR NONLINEAR FORCED VIBRATION EQUATION ON HELICOPTER MAIN ROTOR LOAD

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AN ITERATIVE PARALLEL ALGORITHM OF FINITE ELEMENT METHOD

In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.

A necessary and sufficient condition for positive solutions of singular fourth order boundary value problems

This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the monotone iterative technique.Furthermore,the uniqueness of the C3 positive solution,and the iterative sequence of the C3 positive solution are also obtained.

EXISTENCE THEOREMS OF EXTREMAL SOLUTIONS FOR A CLASS OF NONLINEAR INTEGRO－DIFFERENTIAL EQUATIONS

In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .

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.

ITERATION SOLUTION OF THE MIXED FORMULATION IN NONLINEAR FEM

Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. However, the penalty has tobe chosen properly. If it is too large, the matrix equation may become ill-conditioned. Onthe other hand, the matrix equation may give incorrect answer if the penalty is too small.In non-linear regime, the difficulty is more serious because the magnitude order of the matrix varies considerably in the entire loading history. The paper suggests an iteration solution and applies it to non-linear FEM of rubber-like hyper-elasticity. This type of analysisis highly non-linear both in physics and in geometry as well as the strong constraint of incompressibility. The iteration solution is demonstrated to possess super precision and excellent convergence characteristics.

On dynamic analysis method for large-scale train-track-substructure interaction

Train–track–substructure dynamic interaction is an extension of the vehicle–track coupled dynamics.It contributes to evaluate dynamic interaction and performance between train–track system and its substructures.For the first time,this work devotes to presenting engineering practical methods for modeling and solving such large-scale train–track–substructure interaction systems from a unified viewpoint.In this study,a train consists of several multi-rigid-body vehicles,and the track is modeled by various finite elements.The track length needs only satisfy the length of a train plus boundary length at two sides,despite how long the train moves on the track.The substructures and their interaction matrices to the upper track are established as independent modules,with no need for additionally building the track structures above substructures,and accordingly saving computational cost.Track–substructure local coordinates are defined to assist the confirming of the overlapped portions between the train–track system and the substructural system to effectively combine the cyclic calculation and iterative solution procedures.The advancement of this model lies in its convenience,efficiency and accuracy in continuously considering the vibration participation of multi-types of substructures against the moving of a train on the track.Numerical examples have shown the effectiveness of this method;besides,influence of substructures on train–track dynamic behaviors is illustrated accompanied by clarifying excitation difference of different track irregularity spectrums.

Groundstate with Zero Eigenvalue for Generalized Sombrero-Shaped Potential in N-Dimensional Space

Based on an iterative method for solving the groundstate of Schrodinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.

Solving method of generalized nonlinear dynamic least squares for data processing in building of digital mine

Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.

The Primordial Principle of Self-Interaction

The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes one primordial field and analyzes the evolution of this field. The key assumption is that only the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the Principle of Self-interaction and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.

Theoretical Computation of Nonlinear System Equations of Heavier Pellets Movements for Two Phase Flow

This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.

ITERATIVE POSITIVE SOLUTIONS FOR SINGULAR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEM

By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.

ON SOLUTIONS OF TWO-SCALE DIFFERENCE EQUATIONS

This paper is concerned with solutions of the following two-scale difference equations: f(x)=NΣ anf(2x-n). The conditions for the solvability and the iteractive solvability of this kind ofequstions in certain spaces are obtained respectively.

Quasi-periodic Solutions for the Derivative Nonlinear Schrdinger Equation with Finitely Differentiable Nonlinearities

The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.

THE SYMMETRIC POSITIVE SOLUTIONS OF 2n-ORDER BOUNDARY VALUE PROBLEMS ON TIME SCALES

In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.