NRE 6758: Numerical Methods In Mechanical Engineering


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.
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
  2. Finite Difference Approximations
    • Ordinary Differential Equations
    • Partial Differential Equations
    • Order of Error
  3. Eigenvalue Problems
    • Orthogonality Principal
    • Expansion Theorem
    • Inverse Power Method
    • Jacobi Method
  4. Mid-Term Exam
  5. 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
  6. Initial Value Partial Differential Equations
    • Parabolic Systems
    • Hyperbolic Systems
  7. Final Exam
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