Finite Difference–Collocation Method for the Generalized Fractional Diffusion Equation
Fractal and Fractional, 2022 In this paper, an approximate method combining the finite difference and collocation methods is studied to solve the generalized fractional diffusion equation (GFDE).
Sandeep Kumar +4 more
doaj +1 more source
THE IMPROVEMENT AND REALIZATION OF FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD
Авіаційно-космічна техніка та технологія, 2021 The Lattice Boltzmann Method (LBM) is a numerical method developed in recent decades. It has the characteristics of high parallel efficiency and simple boundary processing. The basic idea is to construct a simplified dynamic model so that the macroscopic
Yifang Sun +3 more
doaj +1 more source
Valuation of the Convertible Bonds under Penalty TF model using Finite Element Method [PDF]
arXiv, 2023 In this paper, the TF system of two-coupled Black-Scholes equations for pricing the convertible bonds is solved numerically by using the P1 and P2 finite elements with the inequality constraints approximated by the penalty method. The corresponding finite element ODE system is numerically solved by using a modified Crank-Nicolson scheme, in which the ...
arxiv
The Compact Finite Difference Method of Two-Dimensional Cattaneo Model
Journal of Function Spaces, 2020 In this paper, we propose and analyze the compact finite difference scheme of the two-dimensional Cattaneo model. The stability and convergence of the scheme are proved by the energy method, the convergence orders are 2 in time and 4 in space.
Yating Huang, Zhe Yin
doaj +1 more source
Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations [PDF]
, 2012 This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D. The goal of the paper is to extend the successful framework of monotone, consistent, and stable finite difference ...
arxiv +1 more source
A Nodal Immersed Finite Element-Finite Difference Method
SSRN Electronic Journal, 2022 The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. This method uses a finite element (FE) method to approximate the stresses and forces on a structural mesh and a finite difference (FD) method to approximate the momentum of the entire fluid ...
David R. Wells +3 more
openaire +3 more sources
A comparison between the Shooting and Finite-Difference Method in solving a Nonlinear Boundary Value Problem found in the context of light propagation [PDF]
arXiv, 2017 The shooting and finite-difference method are both numeric methods that approximate the solution of a BVP to a given accuracy. In this report both methods were implemented in Matlab and compared to each other on a BVP found in the context of light propagation in nonlinear dielectrics.
arxiv
Elasticity of Diametrically Compressed Microfabricated Woodpile Lattices
Advanced Engineering Materials, EarlyView.Modulus–porosity relationship is derived for woodpile lattices with struts under diametrical compression. The formula presented here that Young's modulus is proportional to the square of the volume fraction E˜ρ2$E \sim \left(\rho\right)^{2}$ is shown to be consistent with computations and laboratory experiments on 3D‐printed samples.
Faezeh Shalchy, Atul Bhaskar
wiley +1 more source
Verification of Binomial theorem and Chu-Vandermonde convolution by the finite difference method [PDF]
arXiv, 2011 In this note, we show that Binomial theorem and Chu-Vandermonde convolution can both be verified by the finite difference method.
arxiv
A numerical method for solving elliptic equations on real closed algebraic curves and surfaces [PDF]
arXiv, 2023 There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability between finite element method and computer aided design (CAD) software.
arxiv