# Numerical Methods: Finite difference approach

By Prof. Ameeya Kumar Nayak   |   IIT Roorkee
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
PRE-REQUISITES : Numerical Methods Basic Knowledge
INDUSTRY SUPPORT : TCS, Intel, General Electric, General Motors, ABB, Nuclear Industries, etc

Learners enrolled: 1975

### SUMMARY

 Course Status : Completed Course Type : Core Duration : 4 weeks Start Date : 27 Jan 2020 End Date : 21 Feb 2020 Exam Date : 29 Mar 2020 Enrollment Ends : 03 Feb 2020 Category : Mathematics Level : Postgraduate
This is an AICTE approved FDP course

### 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
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.

### BOOKS AND REFERENCES

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.

### Prof. Ameeya Kumar Nayak

IIT Roorkee
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 CERTIFICATE

• The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
• The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 29th March 2020, Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
• 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. If there are any changes, it will be mentioned then.
• Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE:

• Average assignment score = 25% of average of best 3 assignments out of the total 4 assignments
given in the course.
• Exam score = 75% of the proctored certification exam score out of 100
• Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75.
• If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
• 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.
• Only the e-certificate will be made available. Hard copies will not be dispatched.