scholarly journals Application of the finite element method to solving the duffing equation of ground motion

2020 ◽  
Vol 26 (1) ◽  
pp. 65-71
Author(s):  
Godwin C.E. Mbah ◽  
Kingsley Kelechi Ibeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Duffing Equation ◽  
Weight Functions ◽  
Algebraic Equations ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Minimization Technique ◽  
The Galerkin Method ◽  
Element Method

In this paper, we applied the Galerkin Finite Element Method to solve a damped, externally forced, second order ordinary differential equation with cubic nonlinearity known as the Duffing Equation. The Galerkin method uses the functional minimization technique which sets the equation in systems of algebraic equations to be solved. Various simulation on the effect of change on some parametric values of the Duffing equation are shown. Keywords: Galerkin Finite Element Method, stiffness matrix, Duffing Equation, shape functions, basis functions, weight functions.

scholarly journals Numerical study of Fisher's equation by a Petrov-Galerkin finite element method

1991 ◽  
Vol 33 (1) ◽  
pp. 27-38 ◽  
Author(s):  
S. Tang ◽  
R. O. Weber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Galerkin Finite Element Method ◽  
Linear Diffusion ◽  
Galerkin Finite Element ◽  
Fisher’S Equation ◽  
Nonlinear Reaction ◽  
Fisher's Equation ◽  
Element Method

AbstractFisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.

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