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Department:
MATH
Course Number:
4641
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Not currently offered
Introduction to the numerical solution of initial and boundary value problems in differential equations.
Prerequisites:
Course Text:
No text
Topic Outline:
- Numerical methods for initial value problems Euler methods One-step and multi-step methods Consistency, stability, accuracy, accumulation of error, stiffness Stepsize selection and estimation of the error
- Background material in two-point boundary value problems of ordinary differential equations: existence for linear problems, stability and regularity of solutions. Numerical methods for two point boundary value problems Discussion of boundary conditions One-step schemes, collocation Consistency, stability, error, and convergence Equi-distribution of error and mesh selection
- Numerical solution of the heat equation Method of lines Implicit and explicit methods and the C.F.L.\ condition Consistency, stability, error and convergence
- Implementation issues Advanced iterative methods for linear systems Using structure in linear systems Advanced issues in numerical solution of nonlinear systems
- Numerical solution of eigenvalue problems Approximation of the principle eigenvalue Approximation of all eigenvalues Approximation of eigenfunctions
- Advanced methods for solving matrix eigenvalue problems Householder matrices and orthogonal transformations, reduction of symmetric matrices to tridiagonal form