Application of Taylor Matrix Method to the Solution of Longitudinal Vibration of Rods

Mathematical and Computational Applications

Çevik, Mehmet¹ 

关键词: Taylor matrix method;    Longitudinal vibration;    Numerical solution;    Partial differential equation;   

DOI  :  10.3390/mca15030334

学科分类：计算数学

来源: mdpi

【 摘 要 】

The present study introduces a novel and simple matrix method for the solution of longitudinal vibration of rods in terms of Taylor polynomials. The proposed method converts the governing partial differential equation of the system into a matrix equation, which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Then the solution is obtained easily by solving these matrix equations. Both free and forced vibrations of the system are studied; particular and general solutions are determined. The method is demonstrated by an illustrative example using symbolic computation. Comparison of the numerical solution obtained in this study with the exact solution is quite good.

【 授权许可】

CC BY