Math 467/567 - Scientific Computation - Spring 2010
Dr. Radu C. Cascaval

 

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Notes
 
        
 
  Lecture 1   Wed 1/20 | Introduction to PDEs and their solutions  
 
  Lecture 2   Mon 1/25 | Finite difference scheme for the 1D heat equation  
 
  Lecture 3   Wed 1/27 | The Theta Method  
 
  Lecture 4   Mon 2/1 | Consistency. Stability via Fourier Analysis  
 
  Lecture 5   Wed 2/3 | Convergence and Error Analysis  
 
  Lecture 6   Mon 2/8 | Maximum Principle. Other Boundary Conditions  
 
  Lecture 7   Wed 2/10 | Variable Coefficient Parabolic Equations  
 
  Lecture 8   Mon 2/15 | Parabolic equations in 2D  
 
  Lecture 9   Wed 2/17 | Parabolic equations in 2D  
 
  Lecture 10   Mon 2/22 | Explicit and Implicit Schemes  
 
  Lecture 11   Wed 2/24 | ADI methods for 2D and 3D heat eqs. (Douglas 1962)  
 
  Lecture 12   Mon 3/1 |Hyperbolic equations in 1D. Characteristics.  
 
  Lecture 13   Wed 3/3 | CLF condition.The upwind scheme.  
 
  Lecture 14   Mon 3/8 | The Lax-Wendroff method. Conservation Laws  
 
  Lecture 15   Wed 3/10 | Error Analysis of the Upwind Scheme  
 
  Lecture 16   Mon 3/15 | Finite Volume Scheme.Box scheme
  
 
  Lecture 17   Wed 3/17 | Leap-Frog scheme. Dispersion errors  
          3/22-3/27 | Spring Break  
 
  Lecture 18   Mon 3/29 | Reviw for Midterm Exam  
          Wed 3/31 | Midterm Exam  
 
  Lecture 19   Mon 4/5 | Lax Equivalence Theorem  
 
  Lecture 20   Wed 4/7 | Von Neumann Stability  
 
  Lecture 21   Mon 4/12 | Finite Element Method. Introduction  
 
  Lecture 22   Wed 4/14 | Basics of Functional Analysis  
 
  Lecture 23   Mon 4/19 | Lax- Milgram Lemma. Variational Formulation  
 
  Lecture 24   Wed 4/21 | Error Estimates for FEM  
 
  Lecture 25   Mon 4/26 | Implementation of FEM  
 
  Lecture 26   Wed 4/28 | Algorithms for Solving Linear Systems  
 
  Lecture 27   Mon 5/3 | Convergence of Iterative Methods  
 
  Lecture 28   Wed 5/5 | Conjugate Gradient Method