Numerical Methods for Differential Equations (Math 567)

Boise State University, Dept. of Mathematics

Textbook : Finite difference Methods for Ordinary Differential Equations (R. J. LeVeque)

Semesters Taught : Fa16, Fa17

This course will introduces students to methods for solving partial differential equations (PDEs) using finite difference methods.

Topics

  • Finite difference approximations of differential operators.
  • Local and global truncation error; numerical consistency, stability and convergence
  • The Fundamental Theorem of Finite Difference Methods.
  • Steady state and boundary value problems
  • Numerical time stepping methods for ordinary differential equations, including forward Euler, backward Euler, and multi-step and multi-stage (e.g. Runge-Kutta) methods.
  • The time dependent heat equation (an example of a parabolic PDE), with particular focus on how to treat the stiffness inherent in parabolic PDEs. Method of lines discretizations. Lax-Equivalence Theorem; Lax-Richtmeyer Stability.
  • Numerical methods for PDEs describing wave-like motion (hyperbolic PDEs).
  • Numerical methods for mixed equations involving hyperbolic, parabolic and elliptic terms
  • Brief introduction (if time permits) to finite volume methods for the discretization of conservation laws derived from physical principles.