# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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# Postgraduate Course: Numerical Partial Differential Equations with Applications (MATH11191)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 11 (Postgraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 Summary This course introduces the numerical discretisation of partial differential equations. A number of different partial differential equations will be considered, and methods for yielding approximate numerical solutions will be studied. The course makes significant use of tools from linear algebra, and will include an extended piece of coursework which will apply principles developed in the course to write a numerical solver for a partial differential equations problem. Course description This course introduces the numerical discretisation of partial differential equations. A number of different partial differential equations will be considered, and methods for yielding approximate numerical solutions will be studied. The course makes significant use of tools from linear algebra, and will include an extended piece of coursework which will apply principles developed in the course to write a numerical solver for a partial differential equations problem. - Finite difference discretisation - The method of lines - Consistency, stability, and convergence - Methods for proving numerical stability - Galerkin finite element discretisation - Boundary conditions - Discretisation matrices - Writing numerical solvers for partial differential equations using Matlab
 Pre-requisites Co-requisites Prohibited Combinations Other requirements Students NOT on the MSc in Computational Applied Mathematics programme MUST have passed Honours Differential Equations (MATH10066) AND Computing and Numerics (MATH08065)
 Pre-requisites None High Demand Course? Yes
 Not being delivered
 On completion of this course, the student will be able to: Study solutions to partial differential equations using numerical methodsDiscretise partial differential equations via the finite difference methodDiscretise weak form partial differential equations via the finite element methodUnderstand the principles of discretisation consistency, stability, and accuracyDevelop numerical solvers for partial differential equations
 "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J LeVeque.
 Graduate Attributes and Skills Not entered Keywords NPDEA
 Course organiser Dr James Maddison Tel: (0131 6)50 5036 Email: j.r.maddison@ed.ac.uk Course secretary Miss Sarah McDonald Tel: (0131 6)50 5043 Email: sarah.a.mcdonald@ed.ac.uk
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