6. Multistep Methods: Zero-Stability and Convergence

Learning Objectives

After completing this chapter, you should be able to:

• Understand the concept of numerical stability,

• Find the first, second and overall characteristic polynomials of a linear multistep method,

• Understand the root condition,

• Assess a linear multistep method in terms of

  • zero-stability

  • consistency

  • convergence

• 6.1. An exploratory experiment
• 6.2. Characteristic Polynomials and Root Condition
• 6.3. Zero-Stability, Consistency and Convergence Theorem
• 6.4. Chapter 6 Exercise