Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem by Jing Niu, Ping Li

“…A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. …”
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Reproducing Kernel Method for Fractional Riccati Differential Equations by X. Y. Li, B. Y. Wu, R. T. Wang

“…This paper is devoted to a new numerical method for fractional Riccati differential equations. …”
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Reproducing Kernel Space Method for the Solution of Linear Fredholm Integro-Differential Equations and Analysis of Stability by Xueqin Lv, Yue Gao

“…We present a numerical method to solve the linear Fredholm integro-differential equation in reproducing kernel space. …”
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Microstructure effect of mechanical and cracking behaviors on brittle rocks using image-based fast Fourier transform method by Mingyao Li, Lei Peng, Dejun Liu, Jianping Zuo

“…This phenomenon is also predicted by the proposed numerical method. The results indicate that the proposed numerical method provides an effective approach for analyzing, understanding and predicting the nonlinear mechanical and cracking behaviors of brittle rocks by taking into account the actual microstructure characteristics.…”
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NONLINEAR DYNAMICS ANALYSIS OF DIAPHRAGM COUPLING SYSTEMS WITH ANGULAR MISALIGNMENT by SHENTU LiuFang, ZHAO QingJia, YANG Ping, QIN ShaoBo, SUN YaJun

“…Later,the differential equation is solved by the numerical method. And bifurcation diagram of the systems with the speed changing and the angular misalignment changing are drawn,also the diagrams of displacement response,rotor orbit and phase trajectories under different speeds. …”
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Analysis of Numerical Measure and Numerical Integration Based on Measure by Yinkun Wang, Jianshu Luo, Xiangling Chen

“…We present a convergence analysis for a general numerical method to estimate measure function. By combining Lagrange interpolation, we propose a specific method for approximating the measure function and analyze the convergence order. …”
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Study on Load Sharing Behavior of the Concentric Torque-split Face Gear Transmission for Helicopter by Ning Zhao, Wang Li, Hui Guo, Ruchuan Zhou

“…With the help of numerical method, the influences of the factors of the system on the load sharing behaviors are preliminarily explored. …”
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Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations by Qingyi Zhan, Xiangdong Xie

“…This ensures the feasibility of the numerical method. The practical use of these theorems and the associated algorithms is demonstrated in the numerical computations of the (ω,Lδ)-periodic Lipschitz shadowing orbits of the stochastic logistic equation.…”
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NUMERICAL SIMULATION OF MAGNETIC FIELD STRUCTURE IN CYLINDRICAL FILM SCREEN by G. F. Gromyko, V. T. Erofeenko, G. M. Zayats

“…A numerical method for solving the boundary value problem for a nonlinear magnetostatic equation describing the external magnetostatic field penetration through the cylindrical film coating is developed. …”
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On the Singularity of Multivariate Hermite Interpolation of Total Degree by Zhongyong Hu, Zhaoliang Meng, Zhongxuan Luo

“…Also some regular interpolation schemes are derived, a few of which are proved due to theoretical argument and most of which are verified by numerical method. There are some schemes to be decided and left open.…”
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On destabilising quasi-normal modes with a radially concentrated perturbation by Valentin Boyanov

“…The model is that of a small bump perturbation to the effective potential of linear axial gravitational waves on a Schwarzschild background, and our focus is on three different aspects of the instability: identifying and distinguishing between the two different types of instabilities studied previously in the literature, quantifying the size of the perturbations applied to the system and testing the validity of the pseudospectral numerical method in providing a convergent result for this measure, and finally, relating the size and other features of the perturbation to the degree of destabilisation of the spectrum.…”
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On numerical integration for effective stress assessment at notches by Enrico Maggiolini, Paolo Livieri, Roberto Tovo

“…This paper presents a numerical method for non-local stress assessment by means of a general FE tool and the local stress field. …”
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Fatigue of weld ends under combined in- and out-of-phase multiaxial loading by E. Shams, M. Vormwald

“…In the numerical part of the study, notch stresses were calculated with an idealised weld end model. A numerical method which combines the geometrical and statistical size effect to an integrated approach was used, in order to consider the size effects…”
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Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition by Habtamu Garoma Debela, Gemechis File Duressa

“…An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. …”
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A Second-Order Method for the Numerical Integration of a Size-Structured Cell Population Model by O. Angulo, J. C. López-Marcos, M. A. López-Marcos

“…We propose a new second-order numerical method to attain its solution. The scheme is analyzed and the optimal rate of convergence is derived. …”
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Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition by Wakjira Tolassa Gobena, Gemechis File Duressa

“…A parameter-uniform numerical method is constructed via the nonstandard finite difference method for the spatial direction, and the backward Euler method for the resulting system of initial value problems in temporal direction is used. …”
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Analysis of the Vibration Characteristic of Rolling Bearing-Rotor System of Machine Tool Spindle by Si Zhanfeng, Ma Wei, Li Jishun, Xue Yujun, Yang Fang

“…The system axis path chart,the bifurcation diagram and the Poincare figure are drawn in Matlab and used to analyze the characteristics of the system vibration with the different parameters. The numerical method is used to solve the equations and the displacement values of system vibration are obtained. …”
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Efficient Discrete Interpolation Algorithm and Module Development of Cycloid Gear Profile by Yao Yuchao, Wang Qiliang, Chang Anquan, Jiang Zhongqiu

“…In view of the cycloid gear profile,an efficient discrete interpolation algorithm whose rotation angle intervals are auto adjusted by the curvature and errors are calculated by the numerical method is proposed. Based on this algorithm,a cycloidal tooth profile design module is developed. …”
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Convergence of numerical solution of stochastic differential equation for the self-thinning process by Petras Rupšys

“…In this paper from a practical viewpoint we apply a simple numerical method for solution of the stochastic differential equations by the Milstein's higher order method. …”
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Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids by Huijing Zhan, Mingze Wu

“…In order to solve the numerical method of nonconservative ideal hydrodynamics equations, the viscous perturbation technique for solving nonconservative hydrodynamics equations is improved and tested by solving the Riemann problem. …”
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