11/12/2022 0 Comments Numerical method of relaxationwhere A and b are known and an initial guess for x, x 0 The Gauss-Seidel model is based on the following steps.ġ. It was developed by modifying the Gauss-Seidel iteration model. Frankel in 1950 and was developed to be used on digital computers. SOR was developed in 1950 by David Young and H. SOR on the other hand, while only giving us an approximation, can give us these approximations much faster than Gaussian elimination can. The industry standard for finding exact methods, Gaussian elimination, requires approximately operations to solve the system, which becomes time consuming when n gets big. This is where the successive over-relaxation method (SOR) can come into play. In the real world, time is always something valuable, something no one wants to waste when it comes to solving systems of equations, it can sometimes be better to get a close approximation of the solution than to get the exact solution for this very reason, among others. For this reason, SOR method is important for both researchers and business policymakers. The examples of applications of SOR in Dynamics include study of steady heat conduction, turbulent flows, boundary layer flows or chemically reacting flows. It has applications in Fluid Dynamics, mathematical programming, linear elasticity and machine learning etc. Successive over-relaxation (SOR) is one of the most important method for solution of large linear system equations.
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