CH3023 Computational Techniques Syllabus:
CH3023 Computational Techniques Syllabus – Anna University Regulation 2021
UNIT I NUMERICAL METHODS FOR SYSTEM OF LINEAR ALGEBRAIC EQUATIONS
Gauss elimination, LU decomposition, matrix inversion, Tri-diagonal matrix algorithm, Gauss-Seidel method, Chemical Engineering problems involving solution of linear algebraic equations.
UNIT II NUMERICAL METHODS FOR NON LINEAR ALGEBRAIC EQUATIONS
Introduction, Root finding methods for solution on non-linear algebraic equations: Bisection, Newton-Raphson and Secant methods, System of Non-linear Equations, Chemical Engineering problems involving solution of non-linear equations
UNIT III INTERPOLATION AND NUMERICAL INTEGRATION
Interpolation and Approximation, Newton’s polynomials and Lagrange polynomials, spline interpolation, linear regression, polynomial regression, least square regression, Numerical integration: Trapezoidal rule, Simpson’s rule, integration with unequal segments, Chemical engineering problems involving numerical differentiation and integration.
UNIT IV NUMERICAL METHODS FOR ODES
Euler method – explicit and implicit, Runge-Kutta method – 2nd and 4th order, Boundary value problems – shooting method, Chemical engineering problems involving single and system of ODEs.
UNIT V NUMERICAL METHODS FOR PDES
Introduction to Partial Differential Equations: Characterization of PDEs, parabolic, elliptic and first order hyperbolic equations, explicit and implicit methods, Chemical engineering problems involving the three types of PDEs.
TOTAL: 45 PERIODS
OUTCOMES
On completion of the course, the students will be able to
CO1 – Understand the numerical methods for linear algebraic equations.
CO2 – Identify numerical methods for non linear algebraic equations
CO3 – Identify different methods for interpolation and numerical integration
CO4 – knowledge on the numerical methods for ordinary differential equations
CO5 – understand the basic methods for partial differential equations
TEXT BOOKS
1. Chapra. S. C. & Canale, R. P., “Numerical Methods for Engineers”, Eighth Edition, McGraw Hill, 2021.
2. Gupta, S. K., “Numerical Methods for Engineers, New Academic Science, 2012.
3. Ahuja, P., “Introduction to Numerical methods in Chemical Engineering” 2nd Edition, PHI learning Private Ltd, 2019.
REFERENCE BOOKS
1. R.L. Burden & J. D. Faires, “Numerical Analysis”, 7th Ed., Brooks Coles, 2000.