Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

2012 ◽  
Vol 48 (6) ◽  
pp. 613-687 ◽  
Author(s):  
V. A. Maksimyuk ◽  
E. A. Storozhuk ◽  
I. S. Chernyshenko
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Nonlinear Problems ◽  
Composite Shells ◽  
Linear And Nonlinear ◽  
Difference Methods

scholarly journals The Comparison Study of Hybrid Method with RDTM for Solving Rosenau-Hyman Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 267-274 ◽  
Author(s):  
Derya Arslan
Keyword(s):  
Hybrid Method ◽  
Finite Difference Methods ◽  
Nonlinear Problems ◽  
Comparison Study ◽  
Transform Method ◽  
Differential Transform ◽  
Linear And Nonlinear ◽  
Difference Methods ◽  
Efficiency And Reliability ◽  
Computation Work

AbstractIn this paper, the hybrid method (differential transform and finite difference methods) and the RDTM (reduced differential transform method) are implemented to solve Rosenau-Hyman equation. These methods give the desired accurate results in only a few terms and the approach procedure is rather simple and effective. An experiment is given to demonstrate the efficiency and reliability of these presented methods. The obtained numerical results are compared with each other and with exact solution. It seems that the results of the hybrid method and the RDTM show good performance as the other methods. The most important part of this study is that these methods are suitable to solve both some linear and nonlinear problems, and reduce the size of computation work.

Analysis of Hexagonal Grid Finite Difference Methods for Anisotropic Laplacian Related Equations

2017 ◽  
Vol 10 (3) ◽  
pp. 562-596
Author(s):  
Daniel Lee
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Nonlinear Problems ◽  
Two Dimensional ◽  
Hexagonal Grid ◽  
Hexagonal Grids ◽  
Difference Methods ◽  
Time Dependent Problems ◽  
Mixed Types ◽  
Anisotropic Case

AbstractHexagonal grids are valuable in two-dimensional applications involving Laplacian. The methods and analysis are investigated in current work in both linear and nonlinear problems related to anisotropic Laplacian. Ordinary and compact hexagonal grid finite difference methods are developed by elementary arguments, and then analyzed by perturbation for standard Laplacian. In the anisotropic case, analysis is done through reduction to the standard one by using Fourier vectors of mixed types. These hexagonal seven-point methods, with established theoretic stabilities and accuracies, are numerically confirmed in linear and semi-linear anisotropic Poisson problems, and can be applied also in time-dependent problems and in many applications in two-dimensional irregular domains.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

scholarly journals Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 206
Author(s):  
María Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Stochastic Process ◽  
Finite Difference ◽  
Coming Out ◽  
Finite Difference Methods ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Finite Degree ◽  
Mean Square Stability ◽  
Reaction Models ◽  
Difference Methods

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

A note on the convergence of fuzzy transformed finite difference methods

2020 ◽  
Vol 63 (1-2) ◽  
pp. 143-170 ◽  
Author(s):  
Amit K. Verma ◽  
Sheerin Kayenat ◽  
Gopal Jee Jha
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Difference Methods
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