Aims & Learning |
To introduce students to numerical methods used to simulate engineering problems. After completing this unit, students should be able to: use the numerical methods covered in the unit to solve example applications; design programs to implement numerical algorithms.
Solution of linear equations: Gauss-Jordan elimination. Pivoting. Gaussian elimination. Back-substitution. LU decomposition. Sparse linear systems. Skyline solvers. Iterative methods. Steepest descent. Conjugate gradient method. Pre-conditioned conjugate gradients. Non-linear systems of equations: root finding; one dimensional functions; bisection; secant method; Newton-Raphson; multidimensional Newton-Raphson. Time dependent problems: single step time marching schemes; forward difference, backward difference, midpoint difference, general theta scheme. Stiff systems. Stability. Application of time stepping schemes to circuit modelling. Optimisation (minimization or maximization of functions): one dimensional search. Downhill simplex method in multi-dimensions. Simulated annealing. Evolutionary models.