"This course is a continuation of Numerical Analysis, in which postgraduate students will study advanced algorithms to obtain approximate numerical results for mathematical problems as mentioned below: 1. Numerical methods for solving nonlinear systems: Fixed-point method, Newton's method. 2. Numerical methods for solving initial value problems (single-step methods and multistep methods along with studying error, stability, and convergence of the algorithms). 3. Numerical methods for solving boundary value problems: Shooting method, method of finite differences along with studying error, stability, and convergence of the algorithms. 4. Programming of studied algorithms using MATLAB & Python."