Analisa Galat (numeric)

Numeri c

1. Iterative process/ recursive process 2. Approximate approach

Numerik Vs Analitik Approximate Solution

Analitik Solution

Errors

How To Solve The Problems using Numeric?

 Construct the model from problems and define variables  Eveluate variables to construct simple model  Formulate the model to numerics prosedure  Running the numerics process  Evaluate the solutions

Errors Analization  What is Error conseps?  How to define error?

Approximate solutions Series

 Influence the error  Classification the error

Chopping, Rounding Absolute error, Relatives error

The Taylor Series  If f(x) and all of its derivatives of f(x) defined in [a,b] and if x0 exist in [a,b] so every value x arround x0 can be expaned to the Taylor series.

f '( x0 )( x− x01) f ( x) = f ( 0x ) + 1!

f ''( x0 )( x −x0 2) + 2!

n

f ( x0 )( x ... + + n !

n

The Mc Laurin Series  For every Taylor series that x0 = 0 so every value x arround x0 can be expaned to the Mc Laurine series, that can be expressed by the form:

1

2

n

f '( x0 ) x f ''( x0 ) x f ( x0 ) x f ( x) = f ( x0 ) + + + ... + 1! 2! n!

n

Error concept For every analitic solution a and appoximate solution a’ can be define: 1. Absolute Error (E) E = | a - a’ | 2. Relatives Error (ER)

Relatives Error (E R ) E E R = ........relatives error absolute a E E R = ........relatives error appoximate a' ' ' ar +1 − ar ER = ........relatives error iteratives ' ar +1

STOP! Iteratives must be stoped if 1. The values from two or more iteratives is converges 2.

ER ≤ ES