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Session 8
Numerical Methods

Numerical Differentiation and Richardson Extrapolation

3 hours
Duration
8
Materials
6
Objectives
Session Overview

Finite difference approximations for derivatives, error analysis, and Richardson extrapolation for improved accuracy. Forward, backward, and central difference formulas with applications.

Learning Objectives
By the end of this session, you should be able to:
  • Derive finite difference formulas using Taylor series expansion
  • Implement forward, backward, and central difference approximations
  • Analyze truncation errors and optimal step size selection
  • Master Richardson extrapolation for higher-order accuracy
  • Apply numerical differentiation to partial differential equations
  • Understand the trade-off between truncation and round-off errors
Course Materials
Download materials for offline study and reference
Finite Difference Theory and Derivations (35 pages)
Available material
Error Analysis and Optimal Step Size Studies
Available material
Richardson Extrapolation Implementation
Available material
Partial Derivative Approximation Methods
Available material
Step Size Selection Guidelines
Available material
PDE Application Examples
Available material
Programming Assignment: Derivative Calculator
Available material
Accuracy vs Efficiency Trade-off Analysis
Available material