Formulas

2. What is Numerical Methods ?
Numerical Methods is an approach for
solving mathematical problems using
simple arithmetic operations.
It involves the formulation of model
of physical situations that can be
solved by arithmetical operations.

3. Need of Numerical methods
Mathematical models are a central piece
of science and engineering.
Some models have closed – form solutions,
therefore they can be solved analytically.
Many models cannot be solved analytically
or the analytical solution is too costly to be
practical.
All models can be solved computionally
and the result may not be the exact answer
but it can be uesful.

4. Steps involved to solve
Formulation of Mathematical modelling
Construction of an appropriate numerical method
Implementation of the numerical method
Obtain the solution by solving
Validation of the solution

5. FORMULAS

6. Newton – Raphson Method
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
Lagrange’s Interpolation Method

7. Trapezoidal Rule
  termsremainingtheofsumvalueLastvalueFirst
h
I 2
2

Simpson’s 1/3 Rule
  tremsoddtheofsumtermseventheofsumvalueLastvalueFirst
h
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3

Simpson’s 3/8 Rule
  termsremainingtheofsumthreeofmultiplesvalueLastvalueFirst
h
I (32
8
3


8. Euler’s Method
),(1 nnnn yxfhyy 
Modified Euler’s method
),(1 hyhxfhyy nnnn 
R – K Method
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