Introduction to floating point arithmetic. Numerical stability. Iterative methods for SEL: convergence analysis, stopping criteria. Conditioning. Solution of non-linear equations: Fixed point methods: convergence conditions, stopping criteria. Polynomial interpolation: Lagrange, Newton, Chebyshev polynomials, interpolation error. Curves adjustment. Numerical Integration: Newton-Cotes formulas, composite methods, Romberg method, Gaussian method. Differential equations: Mathematical models. The exponential matrix and solution of linear systems. Nonlinear ODE systems. Stability. Numerical integration of ODE: Taylor, Runge-Kutta, predictor-corrector, exponentials; convergence, A-stability, implementation. Computational methods for PDE. Stochastic simulation. Numerical integration of stochastic equations (EDEs): Euler, Milstein, Ito-Taylor. Types of approximation and convergence. Monte Carlo methods for EDEs. Computer simulation of EDEs. Applications.
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