FAEN 301: Numerical Methods

Matrices and Vector operations, linear homogenous systems, Eigen-vectors and values. Numerical errors, absolute and relative errors, stability and convergence of numerical algorithms. Interpolation Methods: Lagrange polynomials, finite differences, least square approximation. Numerical solutions to Nonlinear Equations: Newton Raphson method, secant, false position, bisection, fixed point algorithm. Numerical Integration: Simpson’s rule, trapezoidal rule, Newton-Cotes method. Numerical solutions to Ordinary Differential Equations: Taylor series method, Euler method, Runge-Kutta method. Numerical solutions to Partial Differential Equations: Second order quasi-linear equations, numerical solutions