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Session 12
Numerical Methods

Boundary Value Problems and Shooting Methods

3.5 hours
Duration
8
Materials
6
Objectives
Session Overview

Numerical methods for boundary value problems including shooting method, finite difference methods, and collocation techniques. Linear and nonlinear boundary conditions.

Learning Objectives
By the end of this session, you should be able to:
  • Understand boundary value problem formulation and solution approaches
  • Implement shooting method for linear and nonlinear boundary value problems
  • Master finite difference methods for BVP discretization
  • Apply collocation methods using orthogonal polynomials
  • Handle various boundary condition types: Dirichlet, Neumann, and mixed
  • Analyze convergence and stability of boundary value problem methods
Course Materials
Download materials for offline study and reference
Boundary Value Problem Theory (38 pages)
Available material
Shooting Method Implementation and Convergence
Available material
Finite Difference BVP Schemes
Available material
Collocation Method Applications
Available material
Boundary Condition Implementation Guide
Available material
Linear and Nonlinear BVP Examples
Available material
Programming Assignment: BVP Solver Package
Available material
Engineering Applications in Heat Transfer and Mechanics
Available material