Numerical Partial Differential Equations I: Finite Difference Methods for Time Dependent PDE
Time/Room: Wed. 15:10 17:0; Thu: 9:10 10:00, Math Building 3175 Lecturer: Chun-Hao Teng
Office: Room 402, Math Building Phone: 2757575 Ext.65120
Prerequisite: Linear Algebra, Fundamental PDE, Basic Computer Programming Skill
• Basic Concepts of Convergence – Consistency, Stability – Lax Theorem
• Model Equations, Schemes (Low-Order) and Analysis – Wave, Heat and Advection-Diffusion Eq.
– Explicit/Implicit Schemes: Lax-Friedrichs, Lax-Wendroff, Leap-Frog, DuFort-Frankel, Crane-Nicholson Semi-Implicit
– Truncation Error Analysis, von-Neumann Condition
• High-Order Schemes
– High-Order Approximations – Phase Error Analysis
• Well Posedness of PDE
– Hyperbolic System of PDE with Constant/Variable Coefficients.
– Parabolic System of PDE with Constant/Variable Coefficients.
• Stability and Convergence of Numerical PDEs
– Stability for Approximations with Constant Coefficients – Energy Methods for Approximations with Variable Coefficients – Splitting Methods
– Hyperbolic Systems and Numerical Methods – Parabolic Systems and Numerical Methods
• Numerical Boundary Conditions – GKS Theorem
– Energy Methods References:
1. Time Dependent Problems and Difference Methods by Bertil Gustafsson, Heinz-Otto Kreiss and Joseph Oliger
2. Finite Difference Schemes and Partial Differential Equations by John C.