Numerical methods and its applications

Numerical methods and its applications

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  NUMERICAL METHODS ANDITS APPLICATIONS
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  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
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  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.
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  Steps involved tosolve  FORMULATION OF MATHEMATICAL MODEL.  CONSTRUCTION OF AN APPROPRIATE NUMERICAL METHOD.  IMPLEMENTATION OF THE NUMERICAL METHOD.  OBTAIN THE SOLUTION BY SOLVING.  VALIDATION OF THE SOLUTION.
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  Why are numericalmethods used in Engineering?  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.
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  APPLICATIONS OF NUMERICALMETHODS
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  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.
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  SCIENTIFIC COMPUTING USING NUMERICALMETHODS  Design and analysis for numerically solving mathematical problems in science and engineering.  Effect of approximations and performs error analysis.  Modern simulations of engineering applications.
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  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.
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  APPLICATION OF NUMERICALMETHODS IN DAY-TO-DAY LIFE
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  MODELLING OF AIRFLOWOVER AIRPLANES ESTIMATION OF OCEAN CURRENTS
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  Shock wave Curve fittingof tabular data
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  Electromagnetics Shuttle tank separation
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  THANK YOU - HAIDERPAREKH