MATH 591 Home Page

• Wednesday, 4
  Introduction to Computational Mechanics
• Friday, 6
  Conservation laws and the one-way wave equation
  
  

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• Monday, 9
  Finite differences for the heat equation
• Wednesday, 11
  Convergence for initial-value problems
  Project #1 Assigned
• Friday, 13
  Convergence for initial-boundary-value problems
  Preliminary Project Ideas Assigned
  
  

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• Monday, 16
  Consistency for initial-value problems
  Preliminary Project Ideas Due
• Wednesday, 18
  Consistency for initial-boundary-value problems
  Consistency for implicit schemes
  Project #1 Due
• Friday, 20
  Stability for initial-value problems
  Stability for initial-boundary-value problems
  Finite differences for the one-way wave equation
  Homework #1 Assigned
  
  

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• Monday, 23
  Lax Equivalence Theorem
  Lax Theorem for initial-value problems
  Lax Theorem for initial-boundary-value problems
  Fourier transform
  Discrete Fourier transform
• Wednesday, 25
  Shift operators
  Symbol of a difference scheme
  
• Friday, 27
  Stability for initial-value problems
  Stability and the symbol
  Stability for PDE's with zero-order terms using the symbol
  Stability for implicit schemes using the symbol
  Homework #2 Assigned
  Homework #1 Due
  
  

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• Monday, 30
  Stability for initial-boundary-value problems
  Matrix norms and spectral radius
  Stability and matrix analysis
  

• Wednesday, 2
  Conservation laws and the one-way wave equation
  Characteristics
  Analytic boundary conditions
• Friday, 4
  Numerical periodic boundary conditions
  Project #2 Assigned
  Homework #2 Due
  
  

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• Monday, 7
  Numerical Dirichlet boundary conditions
  Courant-Friedrichs-Lewy (CFL) condition
• Wednesday, 9
  No class
• Friday, 11
  No class
  
  

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• Monday, 14
  Analytic dissipation and dispersion
  
• Wednesday, 16
  Numerical dissipation and dispersion
  Project #2 Due
  
• Friday, 18
  Numerical dissipation and dispersion for the FTFS scheme (Basic)
  Numerical dispersion for the FTFS scheme (Asymptotic)
  
  
  

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• Monday, 21
  Numerical dissipation and dispersion for the FTFS scheme (Graphical)
  Numerical dissipation and the power spectral density for the FTFS scheme
  
• Tuesday, 22 - Make-up class
  Numerical dissipation and dispersion for the Crank-Nicolson scheme
  Homework #3 Assigned
  Project #3 Assigned
  
• Wednesday, 23
  Order of dissipation
  
• Friday, 25
  Artificial dissipation for an unstable scheme (FTCS)
  
  
  

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• Monday, 28
  Artificial dissipation for a neutrally stable scheme (Crank-Nicolson)
  Modified partial differential equation
  
• Wednesday, 30
  Modified partial differential equation (FTFS)
  Homework #3 Due
  Project #3 Due
  

• Friday, 1
  Analysis of the modified partial differential equation
  Homework #4 Assigned
  Project #4 Assigned
  
  
  

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• Monday, 4
  Modified partial differential equation (Crank-Nicolson)
  Discontinuous solutions
  
• Wednesday, 6
  Discontinuous solutions
  Order and modified equation for advection-diffusion equation (FTCS)
  
• Friday, 8
  Stability for the advection-diffusion equation (FTCS)
  Homework #4 Due
  
  
  

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• Monday, 11
  No class - holiday
  
• Wednesday, 13
  Order, modified equation, and stability for the advection-diffusion equation (Crank-Nicolson)
  Project #4 Due
  
• Friday, 15
  Order, modified equation,and stability for the advection-diffusion equation (Lax-Wendroff)
  Classification of linear systems of partial differential equations
  Consistency, convergence, and stability for linear systems of partial differential equations
  
  
  

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• Monday, 18
  Stability of the explicit scheme for a parabolic linear system
  Theorems on stability of schemes for linear systems
  
• Wednesday, 20
  Stability of the one-sided, Lax-Wendroff, and Crank-Nicolson schemes for linear hyperbolic systems
  
• Friday, 22
  Stability of the FTCS, Lax-Wendroff, and Crank-Nicolson schemes for linear advection-diffusion systems
  
  
  

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• Monday, 25
  Nonlinear scalar problems - Burgers' (inviscid and viscous) equation
  FTCS for Burgers' equation
  BTCS for Burgers' equation
  Linearization for implicit schemes
  Project #5 Assigned
  
• Wednesday, 27
  Lax-Wendroff and Crank-Nicolson for Burgers' equation
  
• Friday, 29
  No class - holiday
  
  
  

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• Monday, 2
  Linearization of Crank-Nicolson for Burgers' equation
  
• Wednesday, 4
  Stability analysis for explicit schemes for scalar equations in 2-D
  Lax-Wendroff scheme for scalar equations in 2-D
  
• Friday, 6
  Approximate factorization and splitting techniques
  Split Lax-Wendroff scheme for scalar equations in 2-D
  
  
  

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• Monday, 9
  ADI techniques: Peaceman-Rachford and Beam-Warming
  
• Wednesday, 11
  Stability analysis for schemes for hyperbolic systems in 2-D
  Stability analysis for schemes for parabolic systems in 2-D
  Simultaneous diagonalization
  
• Friday, 13
  Numerical results for the linear advection-diffusion equation
  Project #5 Due
  
  
  

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Homework and projects

Project #1 Due Wednesday 9-18

Homework #1 Due Friday 9-27

Homework #2 Due Friday 10-4

Project #2 Due Wednesday 10-16

Homework #3 Due Wednesday 10-30

Project #3 Due Wednesday 10-30

Homework #4 Due Friday 11-8

Project #4 Due Wednesday 11-13

Project #5 Due Friday 12-13

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