Backward difference

Numerical analysis. Newton's backward method

1. 05 December 2017 Md. Shakil Ahmed ID. 161-33-3136 Dept. of EEE Md. Rezwanul Haque ID. 163-33-3780 Backward Difference

2. One of a series of quantities obtained from a function whose values are known at a series of equally spaced points by repeatedly applying the backward difference operator to these values; used in interpolation and numerical calculation and integration of functions. And the symbol is ’’ ▼’’ Definition of Backward Difference

3. y 1 , y 2 , y 3 , y 4 1 st backward difference   Backward Difference

4. Backward difference 2 nd backward  

5. Backward Difference = - = - = -

6. Example:01 using Backward Interpolation formula, Find for following data X: 20 25 30 35 40 45 : 354 332 291 260 231 204   x 20 354 -22 -19 29 -37 45 25 332 -41 10 8 8 30 291 -31 20 35 260 -29 2 40 231 -27 45 204 x 20 354 -22 -19 29 -37 45 25 332 -41 10 8 8 30 291 -31 20 35 260 -29 2 40 231 -27 45 204

7. Let, x=42, h=5, =45 p= p= p=-0.6