Numerical Partial Differential Equations I: Finite Difference Methods for Time Dependent PDE

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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

Email: tengch@mail.ncku.edu.tw

Prerequisite: Linear Algebra, Fundamental PDE, Basic Computer Programming Skill

• Introduction

• 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.

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