1 / 5

Numerical Methods and Programming

Numerical Methods and Programming . P. B. Sunil Kumar Department of Physics IIT Mdras Sunil@iitm.ac.in. Class room. Basic structure . (1) C Programing for beginners (2) How accurate and precise are your numerical answers ? (3) Modeling data: Interpolation and fitting

MikeCarlo
Télécharger la présentation

Numerical Methods and Programming

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Numerical Methods and Programming P. B. Sunil Kumar Department of Physics IIT Mdras Sunil@iitm.ac.in

  2. Class room Basic structure • (1) C Programing for beginners • (2) How accurate and precise are your numerical answers ? • (3) Modeling data: Interpolation and fitting • (4) Linear algebra: • (5) Solutions of nonlinear equations and minimization of functions • (6) Numerical differentiation and Integration • (7) Solutions of ordinary differential equations • (8) Solutions of partial differential equations • (9) Discrete and Fast Fourier Transforms Books Numerical Methods for Engineers - S. C. Chapra and R. P. Canale. McGraw-Hill College (2001) Applied Numerical Analysis - C. F. Gerald and P. O. Wheatley Addison Wesley, Boston, 2004. (2004) Computer Oriented Numerical Methods. V. Rajaraman . Prentice-Hall of India Pvt.Ltd (15 Aug 2004) Elementary Numerical Analysis. S. D. Conte and C. de Boor McGraw-Hill College (1972)

  3. C Programming for beginners Basic structure of C program. Different types of variables. Arrays and Pointers , use of functions and pointers to functions, elementary examples using pointers, arrays and functions Accuracy and precision Representation of numbers, numerical arithmetic, condition number and propagation of errors Modeling data Lagrange and Newton interpolation methods, divided difference table. Piece wise polynomial interpolation. Error in polynomial interpolation. Least squares regression. Linear, multiple linear and nonlinear regressions Linear algebra: coupled linear equations, eigenvalues and eigenvectors Elimination method and Pivoting, LU decomposition, Fadeev Leverrier method for characteristic polynomials, power method for eigenvalues. Bairstow's method. Solutions of nonlinear equations and minimization of functions Methods of successive bisection. False position and mid point methods. Secant method. Newton-Raphson scheme.

  4. Numerical differentiation and Integration Divided difference method for differentiation. Newton-Cotes formula. Higher order derivatives. Comparison of errors. Midpoint, Trapezoidal , rectangular and Simpsons rules. Quadrature methods Solutions of ordinary differential equations Euler and predictor corrector methods. Runge Kutta method. Adaptive step size selection. Solutions of partial differential equations Examples of partial differential equations. Implicit and explicit methods. Alternate direction Crank-Nicolson scheme. Discrete and Fast Fourier Transforms

  5. Computer Laboratory Part- A: Basic C Programming Part- B: Familiarizing with the codes corresponding to the topics  covered in class room lectures. Part-C : Problem solving. Curve fitting  Interpolation Numerical Integration: calculation total scattering cross section Differential equations:Coupled harmonic oscillators, heat conduction through a rod and a two dimensional sheet, double pendulum. Eigenvalues and Eigenvectors Fourier Transforms: Diffraction of light, power spectrum.

More Related