MATH 247 - Numerical solutions of Differential Equations

Euler

Cauchy

When: MWF 2-3pm

Where: Academic Support Building B, Room 213

Office: Academic Support Building B, Room 214

Email: roberto DOT deleo AT howard DOT edu

Tentative Syllabus

• Numerical Solution of Ordinary Differential Equations.
  1. one-step and multi-step methods for non-stiff systems of ordinary differential equations,
  2. extrapolation techniques and automatic step size selection,
  3. one-step and multi-step methods for stiff systems of ordinary differential equations and differential-algebraic equations,
  4. single and multiple shooting techniques, finite difference approximations, and the Ritz-Galerkin method for boundary value problems
• Numerical Solution of Partial Differential Equations.
  1. Initial/boundary value problems for parabolic and hyperbolic PDEs (one space and one time dimension).
  2. Explicit finite-difference schemes. Implicit finite-difference schemes. Stability.
  3. Parabolic and hyperbolic PDEs in two and three space dimensions.
  4. Boundary value problems for elliptic PDEs.

Languages used

• MATLAB
• Python
• Any other language registered students wouyld be interested in

Reading list

• L. Burden and J.D. Faires, Numerical Analysis, 7th ed. (2001), Brooks/Cole.
• U.M. Ascher and L.R. Petzold, Computer Methods for Ordinary Diferential Equations and Differential-Algebraic Equations (1998), SIAM.
• L.F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with Matlab (2003), Cambridge.
• J.D. Lambert, Numerical Methods for Ordinary Differential Systems (1991), Wiley.
• R. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (2007), SIAM.
• J. C. Strikwerda, Finite DiÆerence Schemes and Partial Differential Equations (2004), SIAM.