A Novel Method for Nonlinear Boundary Value Problems Based on Multiscale Orthogonal Base

In this paper, a new algorithm is presented to solve the nonlinear second-order differential equations. The approach combines the Quasi-Newton’s method and the multiscale orthogonal bases. It is worth mentioning that the convergence of Newton’s method is verified for solving the nonlinear differential equations. The uniform convergence of the numerical solution as well as its derivatives are also proved. Numerical examples are given to demonstrate the efficiency and feasibility of the proposed method.

Numerical Analysis on Concrete Elastic-Plastic Constitutive under Different Restraints

The fitting curve given by least square method is applied in numerical analyzing. The results from semi-unrestrained and completely restricted modeling show convex deformation and damage on oblique section clearly. Advanced virtual experiment illustrates the differences between loading with displacement and pressure, due to the phenomenon that pressing by force will cause deformation on top surface but displacing load wouldn’t. The fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material. Otherwise, the progress of solving nonlinear function is discussed for designing new numerical analyzing tool, and the frame of programming based on nonlinear method is obtained

A Useful Curve Fitting Method for Concrete Uniaxial Compressive Experiment Data

Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.

Smooth solution to the one-dimensional inhomogeneous non-automorphic Landau–Lifshitz equation

Using the differential–difference method and viscosity vanishing approach, we obtain the existence and uniqueness of the global smooth solution to the periodic initial-value problem of the inhomogeneous, non-automorphic Landau–Lifshitz equation without Gilbert damping terms in one dimension. To establish the uniform estimates, we use some identities resulting from the fact and the fact that the vectors form an orthogonal base of the space .