Journal Article10.1016/J.CAM.2018.02.016
Solving second order non-linear hyperbolic PDEs using generalized finite difference method (GFDM)
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TL;DR: The application of the GFDM to solving different non-linear problems including applications to heat transfer, acoustics and problems of mass transfer are shown.
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About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 01 Feb 2018. The article focuses on the topics: Finite difference method & Moving least squares.
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Citations
Finite difference method for solving fractional differential equations at irregular meshes
TL;DR: A novel meshless technique for solving a class of fractional differential equations based on moving least squares and on the existence of a fractional Taylor series for Caputo derivatives is presented.
66
Fracture mechanics analysis of bimaterial interface cracks using the generalized finite difference method
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Gaussian thermal shock-induced thermoelastic wave propagation in an FG multilayer hybrid nanocomposite cylinder reinforced by GPLs and CNTs
TL;DR: In this article, a modified micromechanical model is proposed to obtain the mechanical and thermal properties of a reinforced functionally graded (FG) multilayer hybrid nanocomposite cylinder for thermoelastic wave propagation analysis with energy dissipation using Green-Naghdi theory.
22
The generalized finite difference method with third- and fourth-order approximations and treatment of ill-conditioned stars
TL;DR: This paper solves 2D and 3D second-order partial differential equations considering the Generalized Finite Difference Method with third- and fourth-order approximations with excellent results both for detecting ill-conditioned stars and for increasing the accuracy of the numerical approximation.
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Finite difference method for solving fractional differential equations at irregular meshes
TL;DR: In this article , a meshless technique for solving a class of fractional differential equations based on moving least squares and on the existence of a fractional Taylor series for Caputo derivatives is presented.
19
References
The approximation power of moving least-squares
TL;DR: The interpolation approximation in R d is shown to be a C∞ function, and an approximation order result is proven for quasi-uniform sets of data points.
The finite difference method at arbitrary irregular grids and its application in applied mechanics
T. Liszka,J. Orkisz +1 more
TL;DR: The FIDAM code as discussed by the authors is a system of computer programs designed for the solution of two-dimensional, linear and nonlinear, elliptic problems and three-dimensional parabolic problems.
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A General Finite Difference Method for Arbitrary Meshes
Nicholas Perrone,Robert Kao +1 more
TL;DR: In this paper, a two-dimensional finite-difference technique for irregular meshes is formulated for derivatives up to the second order, where the domain in the vicinity of a given central point is broken into eight 45 degree pie shaped segments and the closest finite difference point in each segment to the center point is noted.
324
Influence of several factors in the generalized finite difference method
TL;DR: In this paper, the generalized finite difference method (GFD) is used to solve second-order partial differential equations which represent the behavior of many physical processes. And the authors analyze the influences of key parameters of the method, such as the number of nodes of the star, the arrangement of the same, the weight function and the stability parameter in time-dependent problems.
290
A review of numerical methods for nonlinear partial differential equations
TL;DR: A bird’s eye view on the development of numerical methods for solving partial differential equations with a particular emphasis on nonlinear PDEs is provided.