Numerical Analysis (MAGIC066)
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This course is part of the MAGIC core.
Autumn 2011 (Monday, October 10 to Friday, December 16)
No prerequisites information is available yet.
1. Introduction and general overview. 2. Approximation Theory. The Fast Fourier transform. 3. Methods for solving systems of linear and nonlinear equations. Gauss elimination, pivoting. Cholesky factorisation. Conditioning and error analysis. Least squares solution, Schur decomposition, the QR and QZ algorithms. Iterative methods: Jacobi, Gauss-Seidel, SOR. The Conjugate Gradient Method. Krylov subspace methods: Arnoldi algorithm. Conjugate gradient method and GMRES. 4. Numerical methods for ODEs. Taylor series methods. Runge-Kutta methods. Multi-step methods. Boundary value problems: shooting methods, finite difference methods, collocation. Methods for conservative and stiff problems. 5. Numerical methods for PDEs. Finite difference methods for elliptic equations. Parabolic equations: explicit, implicit and the Crank-Nicolson methods. The Galerkin, finite element and spectral methods.
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There will be two assessments for this course with each carrying a weight of 50
MAGIC066: Numerical Analysis Assessment 1
Numerical Analysis - Assessment 2
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