Numerical Methods for Partial Differential Equations
(MTH 572, Spring 2025)
| Time: MW 3:30-4:45pm |
Location: Pastore 219 |
| Instructor: Li Wu |
Office: Lippitt 202K |
| Phone: |
Email: liwuliwu@uri.edu |
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Prerequisite:Calculus courses, Linear Algebra, Numerical Linear Algebra or permission from the instructor.
Reference Books:
Leon Lapidus and George F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering, John Willey and Sons, Inc., 1999.
Alfio Quarteroni and Alberto Valli, Numerical Approximation of Partial Differential Equations, Springer-Verlag, 1994.
G.D. Smith, Numerical Solution of Partial Differential
Equations: Finite Difference Methods, Oxford, 1985.
A.J. Davies, The Finite Element Method: A First Approach, Oxford, 1980.
Claes Johnson, Numerical Solution of Partial Differential Equations
by the Finite Element Method, Cambridge, 1987.
Course Description:
This course is designed for graduate students in mathematics, engineering, finance, and computer science. Based on some fundamental and theoretical results, this course focuses on introducing general techniques, such as finite difference methods and finite element methods, to approach numerical solutions for partial differential equations of practical interests. Special techniques will be discussed for solving problems with singularity, internal and boundary layers. Computer implementation of numerical methods will be presented.
This course covers: finite-difference methods(FDM) and finite-element methods (FEM) for elliptic, parabolic, and hyperbolic partial differential equations; analysis of consistency of schemes, convergence and stability of solutions (will be briefly discussed);
and some topics including boundary element method, finite volume method, methods
of characteristics, some special treatments for singularities.
Grading Policy:
Bi-weekly homework will count 70% of the final grade; A final Project will contribute 30% of the final grade;
Homework and the final project involve computer projects for which
students can use Fortran, C, C++, MatLab, or Mathematica to accomplish.
Enjoy MTH 572 and Enjoy this semester!