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Session 11
Numerical Computation

Adaptive Methods and Error Estimation

4 hours
Duration
8
Materials
6
Objectives
Session Overview

Advanced adaptive algorithms with automatic error control including adaptive quadrature, adaptive ODE solvers, and adaptive mesh refinement for PDEs.

Learning Objectives
By the end of this session, you should be able to:
  • Implement adaptive quadrature with automatic error estimation
  • Master adaptive step size control for ODE solvers with embedded methods
  • Understand a posteriori error estimation techniques
  • Apply adaptive mesh refinement strategies for PDE solutions
  • Design automatic tolerance control and convergence monitoring
  • Implement multi-level and multi-grid adaptive methods
Course Materials
Download materials for offline study and reference
Adaptive Algorithm Theory and Implementation (55 pages)
Available material
Adaptive Quadrature and Integration Methods
Available material
Adaptive ODE Solver Development
Available material
A Posteriori Error Estimation Techniques
Available material
Adaptive Mesh Refinement Algorithms
Available material
Multi-level and Multi-grid Methods
Available material
Convergence Monitoring and Control Systems
Available material
Comprehensive Adaptive Solver Suite
Available material