This ppt helps you to understand the basics of numerical method

1. GALGOTIAS UNIVERSITY
SCHOOL OF MECHANICAL ENGINEERING
PPT’s On NUMERICAL METHODS AND ITS APPLICATION
SUB:-Advanced Numerical and Statistical Methods
SUBMITTED TO, PRESENTED BY,
Mr. SUSHANT SHEKHAR SHUBHESH RANJAN
(DEPT. OF MATHEMATICS) M.TECH(AUTOMOBILE)
YEAR/SEM:-1ST/1ST
ENROLLMENT NO-19032030031

2. NUMERICAL METHODS AND ITS
APPLICATIONS

3. What is Numericalmethod?
 Numerical method is an approach for solving complex
mathematical problems using simple arithmetic
operations.
 It involves the formulation of model of physical situations
that can be solved by arithmetic operations

4. Need of numericalmethod
 Mathematical models are a central piece of science and
engineering.
 Some models have closed-form solutions, therefore they
can be solved analytically. Many models can not be
solved analytically or the analytic solution is too costly to
be practical.
 All models can be solved computationally and the result
may not be the exact answer but it can be useful.

5. Steps involved tosolve
 FORMULATION OF MATHEMATICAL MODEL.
 CONSTRUCTION OF AN APPROPRIATE NUMERICALMETHOD.
 IMPLEMENTATION OF THE NUMERICAL METHOD.
 OBTAIN THE SOLUTION BY SOLVING.
 VALIDATION OF THE SOLUTION.

6. Why are numerical methods used inEngineering?
 Engineers use mathematical modelling which includes various
equations and data to describe and predict the behaviour of
systems.
 Computers are widely used which give accurate results and are
cheap and affordable to all.
 Many software packages are available that can be used to solve
the problems.

7. APPLICATIONS OF NUMERICALMETHODS

8. Application of Numerical Methods in
Mechanical Engineering
 Development of mathematical model representing all important characteristics of the
physical system
 Solution of governing Equation
 Critical Loads for Buckling a column
 Analysis of Natural frequencies of vibrating bar
 Stability of framework under external forces (bridges, houses etc.
 In coal power plant for the modelling of combustion flow
 Re-Entry simulation of space shuttle

9. MODELLING USING NUMERICALMETHOD
 Numerical methods are used in modelling to reduce the
number of prototypes to be constructed.
 It is also used to get the exact or similar design which is
needed in the best way.
Steps to solve:
1. Write your numerical modelling code.
2. Find a simple analytical model and divide into segments.
3. The dimensions are to be specified.

10. SCIENTIFIC COMPUTING USING
NUMERICAL METHODS
 Design and analysis for numerically solving mathematical
problems in science and engineering.
 Effect of approximations and performs error analysis.
 Modern simulations of engineering applications.

11. How it isapplied
 Develop a mathematical problem with your skills and the
requirement.
 Come up with a numerical algorithm.
 Implement the algorithm.
 Run, debug, test the code.
 Visualize and interpret the result.
 Validate the result.

12. APPLICATION OF NUMERICAL METHODSIN
DAY-TO-DAY LIFE

13. MODELLING OFAIRFLOW OVERAIRPLANES
ESTIMATION OF OCEAN CURRENTS

14. Shock wave
Curve fitting of tabular
data

15. Electromagnetics
Shuttle tank separation

16. THANKYOU