Modified Newton Algorithm

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This command is used to construct a ModifiedNewton algorithm object, which uses the modified newton algorithm to solve the nonlinear residual equation. The command is of the following form:

algorithm ModifiedNewton

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NOTES:

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REFERENCES:

Read the page at Wikipedia

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THEORY:

The theory for the ModifiedNewton method is similar to that for the Newton-Raphson method. The difference is that the tangent at the initial guess is used in the iterations, instead of the current tangent. The Modified Newmark method is thus an iterative method in which, starting at a good initial guess <math>U_0\,\!</math> we keep iterating until <math>\Delta U</math> is small enough using the following:

<math> \Delta U = - K_0^{-1}R(U_n),\!</math>

<math> U_{n+1} = U_n + \Delta U\,\!</math>

where:

<math>K_0 = \frac{\partial R(U_0)}{\partial U}\,\!</math>

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Code Developed by: fmk