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# Undergraduate Course: Numerical Partial Differential Equations (MATH10044)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 10 (Year 5 Undergraduate) 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. The coursework may include the use of MATLAB examples. Course description The numerical solution of partial differential equations plays a central role in many areas of modern science. This course will introduce the fundamental concepts and methods of numerical partial differential equations. The methods are built up by considering discretisations of prototypical equations: the Poisson equation, diffusion equation, and advection equation. The course will begin with a study of classic finite difference techniques, and will later move on to a consideration of weak form partial differential equations and the finite element method. Syllabus: 1. Finite difference discretisation 2. The method of lines 3. Consistency, stability, and convergence 4. Methods for proving numerical stability 5. Galerkin finite element discretisation 6. Boundary conditions 7. Discretisation matrices
 Pre-requisites Students MUST have passed: Honours Differential Equations (MATH10066) Co-requisites Prohibited Combinations Other requirements None
 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 accuracy
 The suggested textbook for the course is "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J LeVeque.
 Course URL https://info.maths.ed.ac.uk/teaching.html Graduate Attributes and Skills Not entered Keywords NPDE
 Course organiser Dr James Maddison Tel: (0131 6)50 5036 Email: j.r.maddison@ed.ac.uk Course secretary Mrs Alison Fairgrieve Tel: (0131 6)50 5045 Email: Alison.Fairgrieve@ed.ac.uk
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