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Merge pull request #169 from alxbilger/fixnewtonequation
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Fix Newton-Raphson equation
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bakpaul authored Feb 5, 2025
2 parents 8bf891a + bfa733a commit 3b861e3
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2 changes: 1 addition & 1 deletion 30_Components/40_ODESolver/20_Backward/50_StaticSolver.md
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Expand Up @@ -11,7 +11,7 @@ In a static simulation involving elasticity, the linear system that we solve cor

In case of non-linear elasticity, $K_i$ is a linearization which must be updated with regards to the increment of displacement $\delta u_i$. In such cases, several iterations of Newton Raphson are required to find an appropriate approximate solution. In one step of the StaticSolver, the number of Newton Raphson iterations is ruled by the data field **newton_iterations**.

_Reminder_: the [Newton Raphson method](https://en.wikipedia.org/wiki/Newton%27s_method) is an iterative algorithm aiming at finding the solution of the system $f(x)=0"/> where $f(x)"/> is non-linear. At each iteration of Newton Raphson algorithm, we find a new approximate solution:
_Reminder_: the [Newton Raphson method](https://en.wikipedia.org/wiki/Newton%27s_method) is an iterative algorithm aiming at finding the solution of the system $f(x)=0$ where $f(x)$ is non-linear. At each iteration of Newton Raphson algorithm, we find a new approximate solution:

$x^{n+1}=x^n-\frac{f(x^n)}{f'(x^n)}$ where $f'(x^n) = \frac{df}{dx}(x^n)$

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