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Session 11
Numerical Methods

Ordinary Differential Equations: Initial Value Problems

4.5 hours
Duration
8
Materials
6
Objectives
Session Overview

Comprehensive treatment of numerical methods for solving initial value problems including Euler methods, Runge-Kutta methods, multistep methods, and stability analysis.

Learning Objectives
By the end of this session, you should be able to:
  • Implement Euler method and improved Euler method with error analysis
  • Master Runge-Kutta methods of orders 2, 3, and 4 with derivations
  • Understand adaptive step size control and embedded RK methods
  • Analyze stability regions and stiff differential equations
  • Implement multistep methods: Adams-Bashforth and Adams-Moulton
  • Apply predictor-corrector methods for enhanced accuracy and stability
Course Materials
Download materials for offline study and reference
ODE Theory and Numerical Method Derivations (55 pages)
Available material
Runge-Kutta Method Family Implementation
Available material
Adaptive Step Size Control Algorithms
Available material
Stability Analysis and Stiff Equation Treatment
Available material
Multistep Method Implementations
Available material
Comprehensive ODE Solver Project
Available material
Engineering and Physics Application Examples
Available material
Performance and Accuracy Comparison Studies
Available material