standing-o/Numerical_Analysis

My personal MATLAB toolbox for numerical analysis

Numerical Analysis

• My personal MATLAB toolbox for numerical analysis
• May. 12, 2021 ~ Present

1. Numerical solution of first order ODEs

Forward Euler Method - Explicit | Code

y_i+1 = y_i + f(t_i, y_i)Δt + O(Δt²)

• It uses the slope at each point to exgtrapolate and find the next point
• O(Δt²)

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Backward Euler Method - Implicit

y_i+1 = y_i + f(t_i+1, y_i+1)Δt + O(Δt²)

• O(Δt²)

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Midpoint Method

y_i+1 = y_i-1 + 2f(t_i, y_i)Δt + O(Δt³)

• Symmetric method using Taylor expansion that involves only odd powers of Δt
• O(Δt³) -> More accurate
  -> but require special initialization

Reference

[1] Bergara, A. "Finite Difference Numerical Methods of Partial Differential Equations in Finance with MATLAB." Master and Banca (2011).