Handbook

Computational methods are of paramount importance for solving real-world problems in applied mathematics.This unit teaches widely used numerical methods for problems from science, engineering, biology and finance that are modeled by partial differential equations (PDEs). The unit covers numerical methods for PDEs of elliptic, parabolic and hyperbolic type, as well as advanced solution methods for the linear and nonlinear systems of equations that may arise from the discretisation of the PDEs. Topics covered may include finite difference methods, finite element methods, and finite volume methods; iterative and multigrid solvers for linear and nonlinear systems; nonlinear hyperbolic conservation laws; and other topics in numerical PDEs.The concepts of numerical accuracy, stability and efficiency play a central role in the unit. You will receive an introduction to the theory of the numerical methods (with derivations of the methods and some proofs), and will learn to implement the computational methods efficiently. Applications will be covered from various domains such as heat transfer, option pricing, biology, and fluid mechanics.