MATH593 NUMERICAL SOLUT. OF PARTIAL DIFF. EQU.
| Course Code: | 2360593 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. BÜLENT KARASÖZEN |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will gain:
- an ability to apply the a numerical technique for the solution of parabolic, elliptic and hyperbolic partial differential equations
- an ability to identify, formulate, and solve the partial differential equations numerically
- the knowledge on the finite difference technique and its application
- the knowledge on convergence, consistency, stability of the the numerical technique
- the knowledge of truncation error and its order
Course Content
Finite difference method, stability, convergence and error analysis. Initial and boundary conditions, irregular boundaries. Parabolic equations; explicit and implicit methods, stability analysis, error reduction, variable coefficients, derivative boundary conditions, solution of tridiagonal systems. Elliptic equations, iterative methods, rate of convergence. Hyperbolic equations. The Lax-Wendroff method, variable coefficients, systems of conservation laws, stability. Finite volume method.
Course Learning Outcomes
At the end of the course students are expected to:
- identify the type of PDEs
- apply the finite difference technique to parabolic, elliptic and hyperbolic PDEs
- do the stability and convergence analysis of the FDM
- find the truncation error and its order