ENGG701

ENGG701 Advanced Numerical Methods

Course Overview and Description 


ENGG 701 Advanced Numerical Methods (3-0-3)

This course aims at covering advanced methods of numerical analysis. It briefs introduction to numerical computing, approximation and errors which is followed by methods of solving system of nonlinear equations and approximation of functions. Numerical solutions of ordinary differential equations; initial value problems and boundary value problems, simultaneous differential equations, Runga-Kutta methods, finite difference method. Numerical solution techniques for linear, elliptic, parabolic and hyperbolic partial differential equations. Methods will be implemented using toolboxes of MATLAB.

(New developed program-2025)
Course Code: ENGR 704  Course Title: Advanced Numerical Methods

This course aims at covering advanced methods for numerical analysis. It briefs introduction to numerical computing, approximation and errors which is followed by methods of solving system of nonlinear equations and approximation of function. Numerical solutions of ordinary differential equation; initial value problems and boundary value problems, simultaneous differential equation, Runga-Kutta methods, finite difference method. Numerical solution techniques for linear, elliptic, parabolic and hyperbolic partial differential equations. Introduction to some theoretical basics and practical applications of the finite element method in engineering. Methods will be implemented using concurrent coding software.

List of Topics for Advanced Numerical Methods Course:

  1. Introduction to Numerical Computing

     

  2. Concurrent Coding for Numerical Methods
    • Implementation of numerical algorithms using concurrent coding techniques (MATLAB/Python)
  3. Approximation and Error Analysis
    • Types of errors (truncation, round-off, propagation)
    • Error estimation and stability
  4. Methods for Solving Systems of Nonlinear Equations/ Root finding 
    • Iterative methods (Newton-Raphson, Secant, Fixed-Point)
  5. Function Approximation Techniques
    • Polynomial interpolation
    • Least squares approximation
  6. Numerical Solutions of Ordinary Differential Equations (ODEs)
    • Initial Value Problems (IVPs)
    • Boundary Value Problems (BVPs)
    • Simultaneous Differential Equations
    • Runge-Kutta Methods
    • Finite Difference Methods for ODEs
  7. Numerical Solution Techniques for Partial Differential Equations (PDEs)
    • Linear PDEs
    • Elliptic PDEs
    • Parabolic PDEs
    • Hyperbolic PDEs
  8. Finite Difference Methods for PDEs / Introduction to Finite Element Method (FEM)
    • Theoretical basics of FEM
    • Practical applications of FEM in engineering

Intended Learning Outcomes (CILOs):

By the end of the course, students will be able to:

  1. CILO 1: Evaluate advanced numerical methods for solving linear and nonlinear equations, differential equations, and optimization problems.
  2. CILO 2: Develop efficient numerical algorithms using MATLAB and Python.
  3. CILO 3: Critically assess the stability, convergence, and accuracy of numerical solutions.
  4. CILO 4: Apply numerical methods to real-world engineering problems, including AI-based models, IoT systems, and data-driven applications.
  5. CILO 5: Integrate numerical techniques into research projects, demonstrating innovative solutions to complex problems.

Teaching Methodology:

  • Lectures: Detailed theoretical explanations with mathematical derivations and real-world examples.
  • Hands-on Programming / Assignments: Practical sessions using MATLAB and Python for algorithm implementation.
  • Case Studies/ Projects: Regular problem sets and a final research-based project.

Textbook

  • Numerical Methods for Engineers by Steven C. Chapra & Raymond P. Canale
  • Applied Numerical Methods Using MATLAB” by Steven C. Chapra
  • Applied Numerical Methods Using MATLAB” by Won Young Yang, Wenwu Cao, Tae-Sang Chung, and John Morris
  • Week 1: Introduction to Numerical Methods
  • Week 2: Error Analysis and Stability
  • Week 3: Solving Nonlinear Equations
  • Week 4: Systems of Linear Equations
  • Week 5: Numerical Differentiation and Integration
  • Week 6: Ordinary Differential Equations (ODEs)
  • Week 7: Partial Differential Equations (PDEs)
  • Week 8: Optimization Techniques
  • Week 9: Monte Carlo Simulations
  • Week 10: Final Project and Research Integration