Math 228B - Numerical Solution of Partial Differential Equations

Lectures: TuTh 11-12:30 am, 5 Evans

Instructor: J Strain, strain@math.berkeley.edu, 642-3656

Web page: http://math.berkeley.edu/~strain/

Office Hours: Tu 2-4 pm and W 4-5 pm @ 1099 Evans. No office hours Tu 19 April, Tu 26 April, and Th 28 April: instead, office hours 2-5 W 20 April and Th 21 April.

GSI: Jianlin Xia

Web page (where problem set solutions are posted): http://math.berkeley.edu/~jxia/228b/

Office Hours: Wed 2-4 pm in 775 Evans.

Prerequisites: Math 128A or equivalent. Sufficient computer skills to download, compile and modify numerical packages written in Fortran and C. Basic numerical programming in a language such as Matlab, C, Fortran, Perl, ...

Required Texts:

  • J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, 1995.
  • J. W. Thomas, Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations, Springer, 1999.
  • Syllabus: Math 228B will survey the theory and practice of finite difference methods for parabolic, hyperbolic and elliptic partial differential equations. Topics will include: Basic linear partial differential equations and schemes. Convergence, stability and consistency. Practical stability analysis. ADI schemes. Numerical boundary conditions. GKSO theory. Dispersion and dissipation. Theory of nonlinear hyperbolic conservation laws. Entropy conditions and TVD schemes. Relaxation and multigrid for linear elliptic equations.

    Problem Sets:

  • Problem Set 1: Solve exercises 1.3.1, 1.4.2, 1.5.11, 1.6.3, 2.2.1 and 2.3.1 in vol. 1 of Thomas; due Thursday 29 January.
  • Problem Set 2: Solve exercises 2.3.5, 2.3.6, 2.4.1, 2.4.2 and 2.6.1 in vol. 1 of Thomas; due Thursday 5 February.
  • Problem Set 3: Solve exercises 3.1.2, 3.1.3, 3.2.3, 3.4.1 and 3.4.2 in vol. 1 of Thomas; due Thursday 12 February.
  • Problem Set 4: Solve exercises 4.2.7, 4.2.8, 4.3.2, 4.4.1, 4.4.5 and 4.4.11 in vol. 1 of Thomas; due Thursday 19 February.
  • Problem Set 5: Solve exercises 5.3.2, 5.3.3, 5.4.4, 5.6.7, 5.6.10 and 5.6.12 in vol. 1 of Thomas; due Thursday 26 February.
  • Problem Set 6: Solve exercises 5.8.5, 5.8.7, 5.9.1, 5.9.2, 6.2.6 and 6.3.1 in vol. 1 of Thomas; due Thursday 4 March.
  • Problem Set 7: Solve exercises 9.2.2, 9.2.6, 9.2.8, 9.2.12, 9.3.2 and 9.4.3 in vol. 2 of Thomas; due Thursday 1 April (no fooling).
  • Problem Set 8: Solve exercises 9.7.10, 9.7.11, 9.7.12, 9.7.17, 9.7.20, 9.7.21 and 9.7.32 in vol. 2 of Thomas; due Thursday 15 April (tax-free).
  • Problem Set 9: Solve exercises 10.3.1, 10.5.4, 10.5.6, 10.5.10, 10.5.15 and 10.5.18 in vol. 2 of Thomas; due Thursday 22 April.
  • Problem Set 10: Solve exercises 10.5.19, 10.5.20 and 10.12.1 in vol. 2 of Thomas; due Thursday 29 April.
  • Problem Set 11: Solve exercises 10.13.1, 10.10.7 and 10.10.11 in vol. 2 of Thomas; due Tuesday 11 May.