作图法求解实验方程要注意的问题

通过分析实验方程参数不确定度的实例，指出了作图法注解实验方程应注意的几个问题。     

用计算器求解实验方程的不确定度

给出用计算器求解实验方程不确定度的方法, 简便易行．     

作图法研究物理实验数据处理中的线性回归问题

用作图的方法研究物理实验数据处理中的一元线性回归问题,通过作回归直线和标准差平行四边形,求出线性回归方程标准差和相关系数。     

作图法求直线斜率取点远近的探讨

本文以力敏传感器定标数据为例,使用origin软件对数据进行了直线拟合。在作图法拟合的直线上,选取离中值点较远处和较近处坐标点,计算得到靠近两端离中值点较远处坐标点斜率的误差远小于离中值点较远处坐标点斜率,通过误差杆理论分析了其中的缘由。     

作图法在实验数据处理中的作用

作图法的优点是简便、形象、直观，有取平均值的效果，便于发现测量错误．利用作图法处理实验数据，有利于进一步研究实验结果，求出某些物理量，建立关系式等．在中学物理实验中，作图法在部分实验数据处理中有着广泛的应用。     

作图法处理数据及其不确定度的评定

作图法处理数据是大学物理实验训练内容之一。本文强调了作图法的作用与优点,较详尽的说明了作图法的具体规范以及如何用图线上的直线与斜率导出物理量的方法,最后给出作图法处理数据不确定度的一般方法。     

为什么要用作图法处理实验数据

"能用图像描述实验数据"是《普通高中物理课程标准(2003年版)》和《普通高中物理课程标准(2017年版)》的共同要求,也是较老版《教学大纲》用"逐差法"处理实验数据的重大变化,文章主要探讨为什么要发生这样的变化.     

大学物理实验中测量不确定度的评定与表示

介绍不确定度的有关概念，并结合具体实验教学的测量模型，提出了对不确定度Ａ类分量及Ｂ类分量评定的合理简化，给出了两种不同简化模式下展伸不确定度的表示式。     

在工科物理实验中的不确定度

本文简单叙述了现代不确定度评定的要点以及在工科物理实验中不确定度评定的方法，并举例进行了比较。     

误差杆的概念及其应用

介绍了误差杆的概念及其在实验作图中的应用。     

Transformation methods for solving nonlinear field equations

The collection of extended canonical transformations of first-order contact manifolds is studied. This collection is shown to form a group under target-source composition and to contain the group of all first prolongations of point transformation of the underlying graph space and all isogroups of completely integrable horizontal ideals. Extended canonical transformations are compared and contrasted with Bäcklund transformations. These results are used to construct an extended Hamilton-Jacobi method for systems of nonlinear PDE. The collection of all extended canonical transformations is also shown to contain infinitely many one-parameter families of transformations, but there is no Lie group structure that contains these one-parameter families, in general. Conditions are obtained under which a one-parameter family of extended canonical transformations will map a solution of the fundamental ideal that characterizes a given system of PDE into a one-parameter family of solutions. These results are applied to the -Gordon equation _x1 = () and to the Navier-Stokes equations.     

Analytical mechanics methods for solving Whittaker equations

The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange--Noether method, Hamilton--Poisson method and potential integral method.     

On spectral methods for solving nonlinear acoustics equations

Two very efficient methods for obtaining approximate solutions to nonlinear acoustics equations are discussed. I proposed these methods earlier, but they are still little known. The first method is based on expanding an unknown function into a Taylor series with respect to the coordinate (evolution variable) and on approximate summation of the terms of this series in all orders up to the infinite order. This series can be summed completely only in particular cases, e.g., for a simple wave. It has been noted that the partial summation technique is implemented more easily if all the terms of the series are represented as corresponding topological diagrams. The second method is based on introducing a “nonlinear” phase delay (proportional to the wave amplitude) for the temporal variable in linear solutions of the problem. The application technique of these methods is illustrated by obtaining approximate solutions of the Burgers equation.     

A comparison between Lanczos and moment methods

A simple procedure is suggested for generating the 2n - 1 Lanczos tridiagonal elements from the 2n - 1 moments of any hamiltonian with regard to a given starting vector. The numerical feasibility is studied in the quartic oscillator example.     

A comparison of variational and discrete ordinate methods for solving radiative transfer problems

In this paper, we compare the variational and discrete ordinate methods applied to their simplest representative cases: the 2-step function variational method and the 2-stream approach. It is shown that both methods require minimal computational time. Numerical results of the source functions, intensities and fluxes for the problem of diffuse reflection by different plane-parallel isotropic atmospheres are compared between the two methods. Limitations of both approaches for different single scattering albedos and optical depths are discussed. It is also shown that the variational technique is a more efficient algorithm in handling multi-layer cloud conditions for radiative transfer problems.     

A comparison of approximate methods for solving non-conservative problems of elastic stability

The methods of Ritz, Galerkin, and complementary energy are applied to a nonconservative problem in the theory of elastic stability. The numerical calculations are based upon (i) a variational expression, for which no functional can be determined, and (ii) an adjoint variational principle, for which a functional is established in terms of the variables of the original non-self-adjoint eigenvalue problem and the adjoint problem. The adjoint variational principle yields somewhat more accurate values for the critical load parameter than does the variational expression. In addition, the results obtained by means of the complementary energy method are more precise than the corresponding results obtained from the Ritz and Galerkin methods.     

A method for solving nonlinear equations

A direct method for solving constant coefficient nonlinear evolutional problems of mathematical physics extending the Hirota method to the case of degeneracy of k-parameter is described. An application of this method to the problem of finding the solutions describing coupled states in φ⁴-theory with damping is considered.     

Unified compact ADI methods for solving nonlinear viscous and nonviscous wave equations

In this paper, two unified alternating direction implicit (ADI) methods, based on the combination of fourth-order compact difference for the approximations of the second spatial derivatives with approximation factorization of difference operators, are presented for solving a two-dimensional (2D) and three-dimensional (3D) nonlinear viscous and nonviscous wave equations, respectively. By the discrete energy method, it is shown that their solutions converge to exact solutions with an order of two in time and four in space in L²- and H¹-norms. Finally, numerical findings testify the computational efficiency of the algorithms.