Chapter 4: Elliptic and Parabolic Problems

Overview

This chapter focuses on numerical methods for elliptic and parabolic partial differential equations relevant to heat transfer and fluid flow.

Learning Objectives

  • Classify partial differential equations
  • Discretize elliptic and parabolic PDEs
  • Implement solution algorithms for heat transfer problems
  • Handle boundary conditions

Topics

4.1 Classification of PDEs

4.2 Elliptic Problems (Steady-State Heat Transfer)

4.3 Parabolic Problems (Transient Heat Transfer)

4.4 Finite Difference Discretization

4.5 Stability and Convergence