Course Unit Code : AMAT 41773
Course Title : Advanced Computational Mathematics
Pre-requisites : AMAT 22582
Learning outcomes:
Upon successful completion of the course unit the student will be able to:
- Investigate the criteria such as convergence, rate of convergence, accuracy and appropriate consistency and stability
- Apply numerical algorithms to solve initial boundary value problems in the form of partial differential equations.
Course Content:
Finite Difference Methods: Introduction to finite difference schemes, Solve parabolic, hyperbolic and elliptic partial differential equations, Dirichlet boundary conditions and Neumann boundary conditions, Convergence: Consistency and Stability using Von Neumann Analysis, Lax Equivalent Theorem.
Finite Element Methods: Variational formulation of problem-classification of partial differential operators, Weighted residual methods: Collocation method, least square method, Galerkin method.
Practicals: Implement Finite difference Schemes using an appropriate software, Implement Finite element schemes using Free FEM++
Method of Teaching and Learning : A combination of lectures and tutorial discussions
Assessment : Based on tutorials, presentation, tests and end of course examination
Recommended Textbook:
- Burden, R.L., Faires, J.D, Burden, M.L. Numerical Analysis (10e), Cengage Learning. (2015).
- J. Davies, Finite Element Method: An Introduction to Partial Differential Equations (2e), OUP Oxford (2011)
- M. Desai, Finite Element Method with Applications in Engineering. Pearson Education India (2011)
- Pavel Ŝolín, Partial Differential Equations and the Finite Element Method. (2013)