scholarly journals Discretization of Laplacian Operator in Polar Coordinates System on 9-Point Stencil with Mixed PDE’s Derivative Approximation Using Finite Difference Method

2021 ◽  
Vol 2 (3) ◽  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Polar Coordinates ◽  
Laplacian Operator ◽  
Point Stencil ◽  
Derivative Approximation

scholarly journals Modal Analysis of Circular Symmetrical Plates by Means of Generalized Finite Difference Method

2019 ◽  
Vol 17 (3) ◽  
pp. 88-98
Author(s):  
A. E. Mansour
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Modal Analysis ◽  
Difference Method ◽  
Numerical Solutions ◽  
Analysis Procedure ◽  
Machine Design ◽  
Polar Coordinates ◽  
Circular Plates ◽  
Classical Formulation

In this paper, a simplified modal analysis procedure of circular plates procedures (on polar domains) through generalized (modernized) finite difference method (abbreviated next as – FDM) is developed.Generally, circular plates are widely used for a plenty of modern civilian and industrial utilities, machine design and many other purposes. They form a spectrum of elements starting with trains’ bogies along with engine pistons, dampers and up to slabs and roofs over circular-shaped buildings, train stationsand other transportation facilities. Nowadays, FDM predominates the numerical solutions of partial differential equations (abbreviated next as – PDE) not less than the method of finite elements (abbreviated next as – FEM). This is wide-famous mathematical-discretization method that is economic to compute and simple to code, less regarding to computation tools in hands and how powerful/less powerful they are, since it bases on replacing each derivative by a difference algebraic quotient in a classical formulation. In a sense, a finite difference formulation offers a more direct approach to the numerical solution of the PDE especially in polar coordinates domain problems considering curvilinear dimensions that even FEM does not.The generalized approach of FDM considers many parameters less regarded by the classical one.  Consequently, the use of classical approach negatively affects the accuracy of calculation (convergence to the exact solution values) and the tendency of results, the thing been healed by the generalized approach.

scholarly journals A Modified Three-Level Average Linear-Implicit Finite Difference Method for the Rosenau-Burgers Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jiraporn Janwised ◽  
Ben Wongsaijai ◽  
Thanasak Mouktonglang ◽  
Kanyuta Poochinapan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Burgers Equation ◽  
Order Accuracy ◽  
Implicit Finite Difference ◽  
Implicit Finite Difference Method ◽  
A New Technique ◽  
Point Stencil

We introduce a new technique, a three-level average linear-implicit finite difference method, for solving the Rosenau-Burgers equation. A second-order accuracy on both space and time numerical solution of the Rosenau-Burgers equation is obtained using a five-point stencil. We prove the existence and uniqueness of the numerical solution. Moreover, the convergence and stability of the numerical solution are also shown. The numerical results show that our method improves the accuracy of the solution significantly.

HEAT TRANSFER IN LARGE RUBBER ELEMENTS THROUGH OF MODELING BY FINITE DIFFERENCE METHOD

2019 ◽  
Author(s):  
Lucas Peixoto ◽  
Ane Lis Marocki ◽  
Celso Vieira Junior ◽  
Viviana Mariani
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method
Sign in / Sign up

Export Citation Format

Share Document