1. IMPORTANCE & APPLICATION OF NUMERICAL
METHOD IN ENGINEERING
DR. b. C ROy ENGINEERING COLLEGE, DURGAPUR-713206
DEPARTMENT OF COMPUTER sCIENCE & ENGINEERING
(AFFILIATED TO MAULANA AbUL kALAM AzAD UNIvERsITy OF TECHNOLOGy )
NAME:PRIyANkA MANNA
ROLL NO:12000121056
PAPER NAME : NUMERICAL METHOD
PAPER CODE : OEC-IT601A
sEMEsTER: 5TH sEM
2. AGENDA
• WHAT IS NUMERICAL METHOD?
• STEPS INVOLVED TO SOLVE
• WHYARE NUMERICAL METHODS USED IN ENGINEERING?
• APPLICATION OF NUMERICAL METHOD
• EXAMPLE OF NUMERICAL METHOD
• CONCLUSION
3. WHAT Is NUMERICAL METHOD?
• 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. sTEPs INvOLvED TO sOLvE
• Formulation of mathematical model
• Construction of an appropriate numerical method
• Implementation of the numerical method
• Obtain the solution by solving
• Validation of solution
5. WHy ARE NUMERICAL METHODs UsED IN ENGINEERING?
• Engineers use mathematical modelling which includes various equations and
data to describe and predict the behavior 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.
• Numerical methods are crucial in optimization problems, where engineers
aim to find the best possible solution given a set of constraints.
• Numerical methods provide a quicker and more cost-effective way to obtain
solutions, making them valuable in engineering design and analysis.
• It provide a means to assess and control errors in computations. Engineers
can analyze the accuracy of numerical solutions and make adjustments to
improve the reliability of their results
6. APPLICATION OF NUMERICAL METHOD
• Signal Processing: Engineers use numerical methods for processing and
analyzing signals in communication systems, image processing, and audio
processing.
• Robotics and Kinematics: This methods are applied to solve kinematic and
dynamic equations in robotics, aiding in the design and control of robotic
systems.
• Electromagnetic Field Analysis: In electrical engineering, numerical
methods are employed to analyze electromagnetic fields and solve Maxwell's
equations.
• Numerical Integration and Differentiation: Numerical techniques are
applied to approximate integrals and derivatives in cases where analytical
solutions are challenging or not feasible.
7. • Finite Element Analysis (FEA): FEA is widely used for structural analysis
in civil, mechanical, and aerospace engineering.
• Stochastic Modeling:In fields such as finance and reliability engineering,
numerical methods are employed to model and analyze systems with random
or uncertain parameters.
• .
• Optimization Algorithms: Numerical optimization methods are utilized to
find optimal solutions in engineering design problems
8. EXAMPLE OF NUMERICAL METHODs
1.Use trapezoial rule to numerically integrate
f(x) = o.2 + 25 x from a=0 to b=2
Solution:
f(a) = f(0) = 0.2, and f(b) = f(2) = 50.2
I = (b − a) f(b) + f(a)
=(2 − 0) × 0.2 + 50.2 = 50.4
The true solution is
∫f(x)dx = (0.2x + 12.5x2 ) = (0.2 × 2 + 12.5 × 22 ) − 0 = 50.4
Because f(x) is a linear function, using the trapezoidal rule gets the exact
solution.
2
0
2
0
2
2
9. 2. Use the trapezoidal rule to numerically integrate f(x) = 0.2 + 25x + 3x2
from a = 0 to b = 2 .
Solution:
f(0) = 0.2, and f(2) = 62.2.
I = (b − a) f(b) + f(a)
=(2 − 0) × 0.2 + 62.2 = 62.4
The true solution is
∫f(x)dx = (0.2x + 12.5x2 + x3)| = (0.2 × 2 + 12.5 × 2 2+ 23) − 0 = 58.4
The relative error is |²t | = 58.4 − 62.4 × 100% = 6.85%
2
2
2
0 0
2
58.4
