Solving NonLinear Implicit Equations

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Solving Non-Linear Implicit Equations

• R. Edwin García
• redwing_at_purdue.edu

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Stability of the Leap-Frog Method
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Adding Spatial Dependence
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Stability of the Crank-Nicolson Method
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Solving our Discretized System
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Solving the Most General Problem
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The Newton Method
(the physicists way)
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Assume we are very close to finding the solution
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(the engineers way)
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The Error of the Newton Method
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Higher Order Newton
(doing better than Newton(?))
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stop. Otherwise go to
if
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Coupled Non-Linear Problems
Same approach
Assume we are very close to finding the solution
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Coupled Non-Linear Problems

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The Modified Newton Method
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Assume we are very close to finding the solution
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The Secant Method
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Assume we are very close to finding the solution
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