UNIVERSITY OF KERALA - College of Engineering, Trivandrum

08 606.4 ElectiveII ADVANCED COMPUTATIONAL
METHODS
L T P/D Cr
3 1 0 4
Module I
Errors in numerical computation – System of linear algebraic equations –factorization methods – Multiple right
hand sides - Ill-conditioned systems – Symmetric and Banded systems .
Eigen value problems – Power method – Jacobi Method – Practical examples.
System of non linear equations – Newton-Raphson Method.
Module II
Lagrangean and Hermitian interpolation – Quadratic splines - cubic splines (Examples with equal intervals only)
- Data smoothing by least squares criterion – Parabolic and non-polynomial models like exponential model and
power equation – Multiple linear regression.
Taylor series expansion of functions – Solution of first-order ordinary differential equations by use of Taylor
series – Euler’s method and its modifications – Runge-Kutta method.- – Predictor-corrector methods – Milne’s
method and Hamming’s method – Stability of solution.
Higher-order equations of initial value type.by Runge-Kutta method.
Module III
Ordinary differential equations of the boundary value type – Finite difference solution.
Weighted residual methods for initial value problems and boundary value problems – Collocation method –
Subdomain method – Method of least squares – Galerkin’s method.
Partial differential equations in two-dimensions – Parabolic equations – Explicit finite difference method –
Crank-Nicholson implicit method.
Elliptic equations – Finite difference method –- Problems with irregular boundaries.
Note: Importance must be given to structural engineering problems wherever possible.
Assignments must be computer oriented.
References :
1. Chapra S. C. and Canale R. P, Numerical Methods for Engineers,Mc Graw Hill
2. Smith G. D, Numerical Solution to Partial Differential Equations, Oxford University Press.
3. Ketter and Prawel, Modern methods of Engineering Computation Mc Graw Hill .
4. Rajasekharan S , Numerical Methods in Science and Engineering. S.Chand.
5. Numerical Methods for Initial and Boundary value Problems, Rajasekharan S,A.H.Wheeler & Co. Pvt.
Ltd.
6. Terrence J. Akai , Applied Numerical Methods for Engineers, John Wiley & Sons
7. B.S Grewal, Numerical methods for Engineers & scientists, Khanna Publishers
Question paper:
Duration: 3 Hrs.
The question paper consists of Part A and Part B.
Part A is for 40 marks. There will be 8 compulsory short answer questions of 5 marks each covering the entire
syllabus .
Part B is for 60 marks. There will be two questions from each module. The candidate has to answer one
question from each module.
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