About Numerical Methods
The course aims to introduce the students with the primary and basic computational & numerical methods to solve chemical engineering problems. • Chemical engineering, mathematical modeling and computational methods Chemical engineering and mathematical Models Computational methods Problem solving steps using computers Numerical solution and errors Roots of Nonlinear Equations in One Variable Equations Encountered with Example Problem(s) Numerical Methods: Bracketing Methods: Bisection, False Position Open Methods: Fixed Point, Newton-Raphson, Secant Systems of Linear Equations Equations Encountered with Example Problem(s) Review of Matrix Algebra Numerical Methods: Direct Methods: Gaussian Elimination, LU (PLU) Decomposition, Thomas Algorithm Iterative Methods: Jacobi, Gauss-Seidel, SOR Approximation and Curve Fitting Regression and Interpolation Problems Encountered with Examples Least Squares Regression: Simple, Multiple, and General Interpolation: Polynomial (Difference and Lagrange Polynomials) Inverse Interpolation Numerical Differentiation and Integration Problem Encountered with Examples Numerical Differentiation Numerical Integration: Newton-Cotes Formulas, Gaussian Quadrature, Adaptive Quadratures Numerical Solutions of Ordinary Differential Equations (ODEs) Equations Encountered with Example Problems Initial Value (IV) ODEs Single First Order (IV) ODEs Taylor’s Methods Runge-Kutta Methods Multistep Methods Higher Order ODEs and Systems of First Order ODEs Boundary Value ODEs Shooting Method Finite Difference Method Consistency, Stability, Convergence and Stiffness