FINITE DIFFERENCE
APPROXIMATION METHOD
BY GURDEEP SINGH, NIMIT JAIN, SYED SAUD ALI
FINITE DIFFERENCE APPROXIMATION METHODS
 THE MOST COMMON ALTERNATIVES TO THE SHOOTING METHOD ARE
FINITE-DIFFERENCE APPROACHES
 IN THESE TECHNIQUES, FINITE DIFFERENCE ARE SUBSTITUTED FOR THE
DERIVATIVES IN THE ORIGINAL EQUATION, TRANSFORMING A LINEAR
DIFFERENTIAL EQUATION INTO A SET OF SIMULTANEOUS ALGEBRAIC
EQUATIONS.
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM

AT THE INTERIOR MESH POINTS,

THE DIFFERENTIAL EQUATION TO BE APPROXIMATED IS

EXPANDING ‘Y’ IN A THIRD TAYLOR POLYNOMIAL ABOUT EVALUATED
AT
AND
, ASSUMING THAT
WE HAVE
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM
FINITE DIFFERENCE METHOD FOR LINEAR PROBLEM
THANK YOU!
FROM GURDEEP SINGH, NIMIT JAIN, SYED SAUD ALI