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Numerical Methods and Machine Learning for Differential Equations with Applications in Python

Euler Method

First Order Initial Value Problem
Euler Method with Theorems Applied to Non-Linear Population Equations
Problem Sheet 1

Taylor Method

Taylor Method
Problem Sheet 2

Runge Kutta

Example 4th order Runge Kutta
Application of 2nd order Runge Kutta to Populations Equations
Problem Sheet 3 - Runge Kutta

Multistep Methods

Adams Bashforth
- 2 Step Adam Bashforth
Adams Moulton
- 1 Step Adams Moulton
Adams Predictor Corrector
Problem Sheet 4 - Multistep Methods

Consistency, Convergence and Stability

Consistency of a Multistep method
Convergence of a Multistep Method
Stability of a Multistep method
Further Notes on Stability
- Problem Sheet 5 - Consistency, Convergence and Stability

Initial Value Problems Review Questions

Initial Value Problem Review Questions

Boundary Value Problems

Linear Shooting Method

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By John S Butler

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