This course is an advanced course offered to UG/PG student of Engineering/Science background. It contains solution methods for different class of partial differential equations. The convergence and stability analysis of the solution methods is also included . It plays an important role for solving various engineering and sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences.
INTENDED AUDIENCE
UG students of technical universities/colleges It is a core course for UG and PG students both.
PRE-REQUISITES
Numerical Methods Basic Knowledge
INDUSTRY SUPPORT – LIST OF COMPANIES/INDUSTRY THAT WILL RECOGNIZE/VALUE THIS ONLINE COURSE
TCS, Intel, General Electric, General Motors, ABB, Nuclear Industries, etc
3481 students have enrolled already!!
COURSE INSTRUCTOR
Dr. Ameeya Kumar Nayak is Associate Professor in Department of Mathematics at IIT Roorkee and actively involved in teaching and research in the direction of numerical modeling of fluid flow problems for last ten years. His research interests are in the fundamental understanding of species transport in macro and micro-scale confinements with applications in biomedical devices and micro electro mechanical systems. He has authored and co-authored more than 32 peer-reviewed journal papers, which includes publications in Springer,ASME, American Chemical Society and Elsevier journals. He is also active in writing book chapter with reputed international publication house.
COURSE LAYOUT
Week 1: Introduction to Numerical methods, Initial and Boundary value problems, Numerical solution of ODE, Picard’s method, Taylor’s series method, Euler’s method, Modified Euler’s method, Runge-Kutta method.
Week 2: Introduction of PDE, Classification of PDE: parabolic, elliptic and hyperbolic. Boundary and initial conditions, Taylor series expansion, analysis of truncation error, Finite difference method: FD, BD & CD, Higher order approximation, Order of Approximation, Polynomial fitting, One-sided approximation.
Week 3: Parabolic equation in 2D, Explicit & Crank-Nicolson method, Alternating direction Implicit method (ADI), Elliptic equations, Solution of Poisson equation with Example, Successive over Relaxation (SOR) method, Solution of Elliptic equation by using ADI method, Example.
Week 4: Hyperbolic equations, solution using Explicit method, Stability analysis of Explicit and Implicit scheme, Example, Characteristics of PDE, Solution of Hyperbolic equation by using methods of Characteristics, Hyperbolic equation of first order, Lax-Wendroff’s method, Wendroff’s method, stability analysis of method, Example.
SUGGESTED READING 1. Gerald, C. F. and Wheatly, P. O.," Applied Numerical Analysis", 6th Edition, Wesley. 2. Smith, G. D., "Numerical Solution of Partial Differential Equations: Finite Difference Methods", Third Edition Clarendon press Oxford. 3. Chapra, S. C. & Canale, R. P., " Numerical Methods for Engineers " SIXTH EDITION, Mc Graw Hill Publication.
CERTIFICATION EXAM
• The exam is optional for a fee. • Date and Time of Exams: April 28 (Saturday) and April 29 (Sunday) : Morning session 9am to 12 noon; • Exam for this course will be available in one session on both 28 and 29 April. • Registration url: Announcements will be made when the registration form is open for registrations. • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.
CERTIFICATE • Final score will be calculated as : 25% assignment score + 75% final exam score. • 25% assignment score is calculated as 25% of average of Best 3 out of 4 assignments. • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and IIT Roorkee. It will be e-verifiable at nptel.ac.in/noc
