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📙Newton-Raphson Method
Solving ordinary differential equations (ODEs) sometimes requires solving nonlinear equations at one or more points. In this context, the Newton-Raphson method is a powerful numerical tool for approximating solutions to such equations.
This method consists of linearizing a nonlinear equation around an initial guess and then iterating to improve this approximation. It is particularly useful when applying implicit schemes (such as the implicit Euler or Crank-Nicolson schemes), since these often require solving nonlinear equations at each time step.
