This document discusses numerical methods and their applications. It begins by defining numerical methods as approaches for solving complex mathematical problems using simple arithmetic operations. Numerical methods are needed because many models cannot be solved analytically or the analytic solution is too costly. The key steps in solving a problem numerically are formulating the mathematical model, constructing an appropriate numerical method, implementing the method, obtaining a solution, and validating the solution. Engineering applications of numerical methods include modeling mechanical systems, analyzing structural loads and vibrations, and simulating processes like combustion and spacecraft re-entry. Everyday applications include modeling airflow over airplanes, estimating ocean currents, analyzing shock waves, and fitting curves to tabular data like in electromagnetics simulations.

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