ME/NRE/HP 6758: Numerical Methods In Mechanical Engineering

Offered Every Fall and Spring

Credit Hours: 3-0-3
Prerequisites: Graduate standing in engineering or a related discipline
Catalog Description: Numerical methods for solution of engineering problems; initial, eigenvalue, and boundary value problems; computational stability for ordinary and linear partial differential equations.
Textbooks: J. Douglas Faires and Richard L. Burden; Numerical Methods, 7th Edition, Brooks/Cole, 2000.
Instructors: Cassiano de Oliveira
References: A. Jennings; Matrix Computation for Engineers and Scientists, John Wiley
S. Crandall; Engineering Analysis, McGraw-Hill
Hornbeck; Numerical Methods, Prentice Hall
Collatz; Numerical Treatment of Differential Equations, Springer
Conte; Elementary Numerical Analysis
Carnahan, Luther, and Wilkes; Applied Numerical Methods
Froberg; Introduction to Numerical Analysis
Goals: To introduce the student to a number of numerical methods needed for solution to mechanical engineering problems; method for solution appropriate to static or steady state problems, vibration or stability problems and initial value or transient problems are considered.
  1. Solution to Simultaneous Equations
  • Direct Methods: Gaussian Elimination
    • Decomposition Methods
    • Symmetric Systems
  • Iterative Methods: Jacobi
    • Gauss-Seidel
    • SOR
  • Finite Difference Approximations
    • Ordinary Differential Equations
    • Partial Differential Equations
    • Order of Error
  • Eigenvalue Problems
    • Orthogonality Principal
    • Expansion Theorem
    • Inverse Power Method
    • Jacobi Method
  • Mid-Term Exam
  • Lectures 18-23, Initial Value Methods
    • Euler, Central Difference and Trapezoidal Methods
    • Stability Issues
    • Systems of First Order Nonlinear Equations
    • Newmark Method for Second Order Dynamic Problems
  • Initial Value Partial Differential Equations
    • Parabolic Systems
    • Hyperbolic Systems
  • Final Exam
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