With the present development of the computer technology, it is necessary to develop efficient
algorithms for solving problems in science, engineering and technology. This course gives a
complete procedure for solving different kinds of problems occur in engineering numerically.31
At the end of the course, the students would be acquainted with the basic concepts in
numerical methods and their uses are summarized as follows:
The roots of nonlinear (algebraic or transcendental) equations, solutions of large system
of linear equations and eigen value problem of a matrix can be obtained numerically
where analytical methods fail to give solution.
When huge amounts of experimental data are involved, the methods discussed on
interpolation will be useful in constructing approximate polynomial to represent the data
and to find the intermediate values.
The numerical differentiation and integration find application when the function in the
analytical form is too complicated or the huge amounts of data are given such as series
of measurements, observations or some other empirical information.
Since many physical laws are couched in terms of rate of change of one/two or more
independent variables, most of the engineering problems are characterized in the form of
either nonlinear ordinary differential equations or partial differential equations. The
methods introduced in the solution of ordinary differential equations and partial
differential equations will be useful in attempting any engineering problem.
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9+3
Solution of equation –Fixed point iteration: x=g(x) method - Newton’s method – Solution of
linear system by Gaussian elimination and Gauss-Jordon method– Iterative method - GaussSeidel
method - Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by
power method and by Jacobi method for symmetric matrix.
UNIT II INTERPOLATION AND APPROXIMATION 9+3
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s
forward and backward difference formulas.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9+3
Differentiation using interpolation formulae –Numerical integration by trapezoidal and Simpson’s
1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulae –
Double integrals using trapezoidal and Simpsons’s rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step methods: Taylor series method – Euler method for first order equation – Fourth
order Runge – Kutta method for solving first and second order equations – Multistep methods:
Milne’s and Adam’s predictor and corrector methods.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS 9+3
Finite difference solution of second order ordinary differential equation – Finite difference
solution of one dimensional heat equation by explicit and implicit methods – One dimensional
wave equation and two dimensional Laplace and Poisson equations.
TOTAL (L:45+T:15): 60 PERIODS
1. Veerarjan, T and Ramachandran, T., “Numerical methods with programming in C”, Second
Editiion, Tata McGraw-Hill Publishing.Co.Ltd, 2007.
2. Sankara Rao K, “Numerical Methods for Scientisits and Engineers”, 3rd Edition, Printice
Hall of India Private Ltd, New Delhi, 2007.32
1. Chapra, S. C and Canale, R. P., “Numerical Methods for Engineers”, 5th Edition, Tata
McGraw-Hill, New Delhi, 2007.
2. Gerald, C. F. and Wheatley, P.O., “Applied Numerical Analysis”, 6th Edition, Pearson
Education, Asia, New Delhi, 2006.
3. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”, 6th
Edition, Khanna Publishers, New Delhi, 2004.