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104 Subject Code NUMERICAL METHODS 3 1 0 4 Version No. 1.0 Course Prerequisites Objectives 1. This course is organized to expose students to some of the most important, basic computational methods likely to be of great use to engineers 2. The emphasis is mainly on computer oriented numerical methods for solving ordinary and partial differential equations. The students are expected to develop MATLAB / FORTRAN / C programs for the numerical methods and obtain results including graphics Expected Outcome On completion of this course, the student will be able to understand and solve Transcendental/Polynomial equations, system of Linear Algebraic equations, Interpolation and approximation, Differentiation and Integration and find solutions of differential equations by finite difference approximations. UNIT-I Algebra and Transcendental system of equations and Numerical integration Newton-Raphson method - Newton-Raphson method for non-linear equations - solution of system of equations – Secant method - Rate of convergence. Gauss – Seidel method for system of algebraic equations – convergence criterion – positive definite of a matrix - spectral radius of a matrix - tridiagonal system of equations – Thomas algorithm - Numerical integration: Trapezoidal rule, Simpsons 1/3 rd and 3/8 th rules UNIT-II Analysis of data Numerical Differentiation - Langrage Interpolation - Interpolation with cubic splines - General Linear Least squares fit, goodness of fit, correlation, Linear regression Spectral analysis: Discrete Fourier transform, Aliasing and Nyquist frequency - Fast Fourier transform UNIT-III Ordinary Differential Equations Review : Euler and Modified Eulers Methods Initial value problems: Fourth order Runge Kutta Method – Sustems of equations and higher order equations Boundary value problems : The shooting method, characteristic value problems, Finite difference method UNIT-IV Partial Differential Equations 2-Dimensional Laplace and Poisson’s equations – Liebmann’s method, 1-dimensional diffusion equation – explicit method – von Neumann stability condition, Crank-Nicholson implicit method, 1-dimensional wave equation – Explicit method - CFL stability condition UNIT-V Finite difference and finite element methods Rayleigh–Ritz method - Collection and Galerkin methods - Finite elements for ordinary differential equations Text Book 1. M.K. Jain, S.R.K. Iyengar and R.K. Jain (2003), Numerical Methods for Scientific and Engineering Computation, 4 th Edition, New Age International Ltd. 2. C.F. Gerald and P.V. Wheatley (2004), Applied Numerical Analysis, 7 th Edition, Addition-Wesley. References 1. R.J. Schilling and S.L.Harris (2000), Applied Numerical Methods for Engineers using MATLAB and C, Brooks/Cole. 2. Erwin Kreyszig (2004), Advanced Engineering Mathematics, 8 th Edition, John Wiley & Sons (Wiley Student Edison). 3. Steven C. Chapra and Raymond Canale (2001), Numerical Methods for Engineers with Programming and Software Applications, 3 rd Edition, Tata McGraw-Hill Co. Pvt. Ltd. 4. E. Balagurusamy (2005), Numerical Methods, 15 th Reprint, Tata McGraw-Hill Co. Pvt. Ltd. 5. K. Sankara Rao (2005), Numerical Methods for Scientists and Engineers, 2 nd Edition, Prentice-Hall of India Ltd. Mode of Evaluation: Assignments / Seminars / Written Examination Recommended by the Board of Studies on: Date of Approval by the Academic Council: 16.6.2008
