MATH 5373-001. NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS

Days:   Mondays and Wednesdays
Times:   2:30 p.m. - 3:50 p.m.
Location: 102 PKH

Recommended Text:  
Office Hours:     11:00 a.m. - 12:00 noon   Mondays and Wednesdays
  or by appointment
 
Office:     441 PKH
Email:     hristo@uta.edu
Telephone:     (817) 272-5763
Course web-page:     http://www.uta.edu/math/faculty/hristo/teaching/math5373F09.html

GRADING POLICIES

    Grades are based on two course projects. There are no homework assignments, and no exams.

    • Project 1 (40%): A short report about one of the build-in functions in MATLAB: ODE Initial Value Problem Solvers. The report should address the kinds of differential equations problems that the MATLAB ODE solver is designed to solve, the numerical method(s) that it uses, and the advantages/disadvantages of the solver.
    • Project 2 (60%): A short report discussing the numerical solution and the interpretation of the results of a project. The project must be about a real-world problem that is modeled by a differential equation or a system of differential equations. Ideally, the differential model will be related to the thesis/dissertation topic of the student (or will be a problem of a special research interest to the student).

    Both course projects must be orally presented in class.


LEARNING OUTCOMES

        Upon the completion of the MATH 5373 course, students will understand the major mathematical ideas behind the numerical methods for solving differential equations and will have acquired a range of skills in the subject, both for analyzing methods and for applying them. The study goals include: mastering the techniques to solve ordinary differential equations/systems and becoming adept at using MATLAB (MATrix LABoratory language) solvers; having the capability of assessing the reliability of the answers; and being able to make a good choice of method (or methods) for a particular problem.
        Topics covered in MATH 5373 include:

    • Mathematical preliminaries
          Sources of error in computational models
          Machine representation of numbers
          Stability of problems and numerical methods
          Polynomial interpolation
          Numerical differentiation and integration
          Locating roots of equations [AI-6]
          Iterative solutions of linear systems [AI-10]
    • Numerical differential equations/systems
          Euler's method and beyond [AI-1]
          Multistep methods [AI-2]
          Runge-Kutta methods [AI-3]
          Stiff equations [AI-4]
          Error control and adaptive algorithms [AI-5]
          Nonstandard finite difference (NSFD) methods
          Two-point boundary value problems [AI-8]


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