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Solving Systems Equations

Initialization & Iterative Solvers

Published : 25-08-2019

The assignment necessitates the use of Matlab in writing a script that solves a given system using the Gauss Seidel method, Successive Over Relaxation (SOR) method, and Jacobi method. You should then solve a system of linear equations to find the unknown values in vector v using the Gauss Seidel method, Successive Over Relaxation (SOR) method, and Jacobi method.

ANSWER

The response of Single and Two Degree of Freedom

In this project, we will get the chance to implement some numerical techniques for computing the response of a single degree of freedom (SDOF) and the two degrees of freedom (2DOF) systems. There are many integration methods such as the Runge-Kutta method, the Simpson method, and the Gauss quadrature. In order to solve the SDOF and 2DOF, we call the builtinode45 MATLAB function, which uses the Runge-Kutta method.

The response of Single and Two Degree of Freedom              

The response of Single and Two Degree of Freedom                   The response of Single and Two Degree of Freedom               The response of Single and Two Degree of Freedom            

        The response of Single and Two Degree of Freedom             The response of Single and Two Degree of Freedom               The response of Single and Two Degree of Freedom          

  III. Conclusion Comparing the obtained numerical results, in the first case of SDOF all the numerical results are the same in the three cases for v=40, 90, and 140 km/hr. In the case of 2DOF, there a small difference between the solution  and the other one , but it is no remarkable.