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10. Numerical_solution_of_systems_of_nonline

# 10. Numerical_solution_of_systems_of_nonline - 2.8 Set of...

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1/2 2.8 Set of Simultaneous Nonlinear Equations All methods involve iteration. Problems with multiple roots and finding a scheme that converges are common. In applied problems, we usually have an idea of the answer – i.e. some idea of what the root(s) should be. This will give us reasonable initial guesses for the iterative solution process. Illustrate the ideas with an example: Find the solution(s) of 10 2 2 2 = + + z y x eqn 1 2 3 z xy e + = eqn 2 1 2 3 1 x y xyz + = eqn 3 Set up a direct iteration scheme, similar to Gauss-Seidel for linear equations. There are no convergence guarantees. “Solve” eqn 1 for x, eqn 2 for y, eqn 3 for z. We can re-order the three equations, and “solve” them in different ways. These choices will usually affect convergence. Several attempts may be required for success. Consider one step in the iteration. We have numerical values for x old , y old , z old and want to find the new, better values.

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10. Numerical_solution_of_systems_of_nonline - 2.8 Set of...

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