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Numerical Analysis 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
- 1st vs 2nd order Taylor methods

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

Intial Value Problems Review Questions

Initial Value Problem Review Questions

Boundary Value Problems

Linear Shooting Method

Parabolic Equations (Heat Equation)

The Explicit Forward Time Centered Space (FTCS) Difference Equation for the Heat Equation

Elliptic Equations

Finite Difference Methods for the Laplacian Equation
Finite Difference Methods for the Poisson Equation with Zero Boundary
Finite Difference Methods for the Poisson Equation

Hyperbolic Equations (Wave Equation)

Wave Equation

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By John S Butler

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