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

Note: In Spring 2014, this course had BSU catalogue number 566.

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.