### Math 6620: Analysis of Numerical Methods II

#### Textbook and References

Main Textbooks: Kendall Atkinson, An Introduction to Numerical Analysis, Wiley

Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM

References:

Victor S. Ryaben'kii and Semyon V. Tsynkov, A Theoretical Introduction to Numerical Analysis, Chapman & Hall/CRC

John Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM

Arieh Iserles, A First Course in the Numerical Analysis of Differential Equations, Second Edition, Cambridge University Press

Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publications

#### The course

Math 6620 is the second semester of a two semester graduate-level sequence in numerical analysis. The second semester focuses primary on numerical methods for solving differential equations.

#### Homework

Homework will be assigned and collected, and will include theoretical analysis and computational assignments. The computational part should be done using MATLAB, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows. The full set of manuals is on the web in html format. The "Getting Started" manual is a good place to begin and is available in Adobe PDF format.

#### 6620 Tentative Topics:

Topics include numerical solution of nonlinear equations: bisection, Newton's and secant methods, contraction mapping principle; interpolation, numerical integration, numerical solution of differential equations: Runge-Kutta methods, linear multistep methods for initial value problems of ordinary differential equations (ODEs). Introduction to the numerical methods for partial differential equations (PDEs): finite difference and finite element methods.

The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for the course.

• Homework 1
• Homework 2
• Homework 3
• Homework 4
• Homework 5

•