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Home  >  Volume 32 (Nov. 2015)

Finite Element Method for the Numerical Solution of Second-Order Differential Equation for the Vibration of Automotive System by Ayodele Ojo and Ochoche A. Peter (pages 205-210)
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This paper considered Finite Element Method (FEM) as an alternative numerical method to approximate a Second-Order Differential Equation with boundary conditions which was derived from an existing model equation for the vibration of an Automotive system with three (3) arbitrary coefficients (M, C and K). This method discretizes the differential equation into N-elements with (N+1) nodes and then obtained its weak formulation and the basis function, leading to a system of tridiagonal matrix equations. The approximate solution of the differential equation obtained using FEM is in a good agreement with the exact solution of the equation. Thus, the method is incredibly precise and efficient enough to be used for the numerical approximation of Second-Order Differential Equations with arbitrary coefficients.

   Keywords: Finite Element Method,  Discretization, Weak Formulation, Basis function, Thomas algorithm