Numerical Methods in Thermal and Fluid Engineering
(502101)
Teaching Scheme: Examination
Lecture: 3 hrs/week Paper: 100 Marks
Paper Duration: 3 hrs.
1. Linear Algebraic Equations:- Gauss – Elimination, Gauss – Seidel,
LU Decomposition.
2. Roots of equations: - Bisection Method, False position method, Newton – Raphson Method, Muller’s method, Bairstow’s Method.
3. Curve fitting – Least square regression:-
i) Linear regression, multiple linear regressions, polynomial regression.
ii) Non linear regression – Gauss – Newton method, multiple non linear
regression.
4. Interpolation: - Newton’s Divided Difference, Lagrange’s Inverse, Spline,
Hermite Interpolation, Extrapolation technique of Richardson’s Gaunt.
5. Differentiation & Integration:- Divided difference formulae, Romberg integration, Gauss quadrature for double & triple integration.
6. Eigen Values & Eigen Vectors of Matrices – Faddeev- Laeverrier’s method,
Power Method, Householder & Given’s method.
7. Ordinary differential equations:- Euler’s method, Heun’s method, Mid – point
method, Runge – Kutta methods, Multi step Methods - explicit Adams – Bashforth
technique & Implicit Adams – Moulton Technique, Adaptive RK method, Embedded
RK method, step size control. Higher order ODE – Shooting method. Non linear ODE
– Collocation technique.
8. Partial Differential Equations:- Solution of Parabolic and Hyperbolic equations –
Implicit & Explicit Schemes, ADI methods, Non linear parabolic equations-
Iteration method. Solution of elliptic equation – Jacobi method, Gauss – Seidel &
SOR method. Richardson method.
Numerical methods should have orientation in thermal and fluid engineering
Laboratory Practice – Solve eight assignments based on each of the above mentioned unit with programming.
References:-
1. Numerical Methods for Engineers, Steven C Chapra & Raymond P Canale, TMH,
Fifth Edition
2. Applied Numerical Methods, Alkis Constantinides, McGraw Hill
3. Numerical Solution of Differential Equations, M.K. Jain, 2nd Edition, Wiley Eastern.
4. Numerical methods for scientific and engineering computation, Jain, Iyangar,
Jain, New Age International Publishers.
5. Numerical methods in Engineering and Science, Dr. B.S. Garewal, Khanna
Publishers.
Reference http://www.unipune.ernet.in/stud_info/Syllabi/Syllabus_2008.html
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