Free Vibrations of Cylindrical Shells by The Nodal Line Finite Difference Method-Part II-Numerical Examples.(Dept.C)

The article presents the derivation of the resolving equations for the calculation of three-layer cylindrical shells under axisymmetric loading, taking into account creep. The problem is reduced to a system of two ordinary differential equations. The solution is performed numerically using the finite difference method in combination with the Euler method.

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Application of Fuzzy Finite Difference Scheme for the Non-homogeneous Fuzzy Heat Equation

10.21203/rs.3.rs-1003065/v1 ◽

2021 ◽

Author(s):

Samaneh Zabihi ◽

reza ezzati ◽

F Fattahzadeh ◽

J Rashidinia

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Heat Equation ◽

Difference Scheme ◽

Difference Method ◽

Taylor Expansion ◽

Truncation Error ◽

Initial Boundary ◽

Convergence Conditions ◽

Numerical Examples

Abstract A numerical framework based on fuzzy finite difference is presented for approximating fuzzy triangular solutions of fuzzy partial differential equations by considering the type of $[gH-p]-$differentiability. The fuzzy triangle functions are expanded using full fuzzy Taylor expansion to develop a new fuzzy finite difference method. By considering the type of gH-differentiability, we approximate the fuzzy derivatives with a new fuzzy finite-difference. In particular, we propose using this method to solve non-homogeneous fuzzy heat equation with triangular initial-boundary conditions. We examine the truncation error and the convergence conditions of the proposed method. Several numerical examples are presented to demonstrate the performance of the methods. The final results demonstrate the efficiency and the ability of the new fuzzy finite difference method to produce triangular fuzzy numerical results which are more consistent with existing reality.

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Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method

Mathematical and Computational Applications ◽

10.3390/mca23040053 ◽

2018 ◽

Vol 23 (4) ◽

pp. 53 ◽

Cited By ~ 1

Author(s):

Amaneh Sepahvandzadeh ◽

Bahman Ghazanfari ◽

Nader Asadian

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Diffusion Equation ◽

Numerical Solution ◽

Difference Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Mean Square ◽

Numerical Examples ◽

Mean Square Convergence

The present study aimed at solving the stochastic generalized fractional diffusion equation (SGFDE) by means of the random finite difference method (FDM). Moreover, the conditions of mean square convergence of the numerical solution are studied and numerical examples are presented to demonstrate the validity and accuracy of the method.

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Plane Stress Analysis of Simply Supported Rectangular Plates by The Nodal Line Finite Difference Method.(Dept.C)

MEJ. Mansoura Engineering Journal ◽

10.21608/bfemu.2021.171608 ◽

2021 ◽

Vol 14 (1) ◽

pp. 71-79

Author(s):

Youssef Agag

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Stress Analysis ◽

Plane Stress ◽

Difference Method ◽

Nodal Line ◽

Rectangular Plates ◽

Simply Supported ◽

Plane Stress Analysis

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A Newton Linearized Crank-Nicolson Method for the Nonlinear Space Fractional Sobolev Equation

Journal of Function Spaces ◽

10.1155/2021/9979791 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Yifan Qin ◽

Xiaocheng Yang ◽

Yunzhu Ren ◽

Yinghong Xu ◽

Wahidullah Niazi

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Scheme ◽

Difference Method ◽

Stability And Convergence ◽

Sobolev Equation ◽

Numerical Examples ◽

Convergence Orders ◽

Theoretical Results ◽

Crank Nicolson

In this paper, one class of finite difference scheme is proposed to solve nonlinear space fractional Sobolev equation based on the Crank-Nicolson (CN) method. Firstly, a fractional centered finite difference method in space and the CN method in time are utilized to discretize the original equation. Next, the existence, uniqueness, stability, and convergence of the numerical method are analyzed at length, and the convergence orders are proved to be O τ 2 + h 2 in the sense of l 2 -norm, H α / 2 -norm, and l ∞ -norm. Finally, the extensive numerical examples are carried out to verify our theoretical results and show the effectiveness of our algorithm in simulating spatial fractional Sobolev equation.

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