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:

1. Burden, R.L., Faires, J.D, Burden, M.L. Numerical Analysis (10e), Cengage Learning. (2015).
2. J. Davies, Finite Element Method: An Introduction to Partial Differential Equations (2e), OUP Oxford (2011)
3. M. Desai, Finite Element Method with Applications in Engineering. Pearson Education India (2011)
4. Pavel Ŝolín, Partial Differential Equations and the Finite Element Method. (2013)