Numerical methods provide approximations that are useful for solving problems in engineering and sciences. They can be used for structural analysis, traffic simulations, weather prediction, analyzing groundwater and pollutant movement, and estimating water flow. Numerical methods allow engineers to create mathematical models of systems, solve those models using computer programs, and check the results to predict behavior. They are applied to calculate loads on structures, collision avoidance in traffic, temperature and precipitation predictions, and tracking groundwater movement.
3. Numerical methods provide an approximation that is generally good
enough. It is useful in all fields of engineering and physical sciences and
growing in utility in the life sciences and the arts
Movement of planets, stars and galaxies
Investment portfolio management
Quantitative psychology
Simulation of living cells
Airline ticket pricing, crew scheduling, fuel planning
4. Mathematical Modeling: Engineers use mathematical modeling involving
equations and data to describe and predict the behavior of systems.
Using of Model
Check the Results Do it again! IF it’s wrong!
Solution of Mathematical Model
With Computer Program? Which Steps?
Mathematical Model & Design
Searching for Solution Control of the Model
Problem Description
Definition Easy or Hard?
5. Structural Analysis: Structural analysis deals with a calculation of load
coming on the structure and analyzing them. It is a procedure followed to
find and measure the effect of external forces on physical objects like built
structure elements. Numerical method is used to calculate strength,
stiffness, stability and vibration of loads and beams.
6. Traffic Simulations: Collision avoidance, exit position, entrance, turning
point of vehicles are solved by forming mathematical model. Numerical
method is used to solve these mathematical models in traffic simulations.
7. Weather prediction: Numerical method is used to predict weather and
environmental simulations by data assimilation to produce outputs of
temperature, precipitation, and hundreds of other meteorological elements
from the oceans to the top of the atmosphere.
8. Ground water & pollutant movement: Ground water forms a part of the
hydrologic cycle. Numerical method is used to analyze the movement of
ground water and pollutants.
9. Estimation of the amount of water: Numerical method is used to estimate
the amount of water that flows in a river, ocean current during a year.
