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Newton’s Forward Difference Interpolation | Numerical Methods Lab
Numerical Methods - Newton's Forward Interpolation

Lab 3: Newton’s Forward Difference Interpolation Method

Lab 3: Newton’s Forward Difference Interpolation Method

Experiment Information

Experiment: Newton’s Forward Difference Interpolation

Course Code: Numerical Methods (SH202)

Description: Complete lab report covering theory, algorithm, Python implementation and analysis of Newton’s Forward Interpolation method

Prepared by: Important Notes Team

Complete Lab Report PDF

1. Theory of Newton’s Forward Interpolation

1.1 Mathematical derivation and formula

1.2 Finite difference operators

1.3 Error analysis and applications

2. Algorithm

2.1 Step-by-step procedure

2.2 Difference table construction

2.3 Interpolation formula implementation

3. Implementation

3.1 Python code with numpy

3.2 Difference table generation

3.3 Interpolation calculation

4. Observations

4.1 Difference table examples

4.2 Sample calculations

4.3 Error comparison

5. Results

5.1 Interpolated values

5.2 Graphical representation

5.3 Error analysis

6. Discussion

6.1 Advantages and limitations

6.2 Comparison with other interpolation methods

6.3 Applications in engineering problems

Digitized lab report prepared by Important Notes Team

Python Implementation of Newton’s Forward Interpolation

newton_forward_interpolation.py
import numpy as np x=np.array([0,1,2,3,4]) y=np.array([-10,-9,-16,89,234]) n=len(y) D=np.zeros((n,n),dtype=float) D[:,0]=y.copy() for j in range(1,n): for i in range(n-j): D[i,j]=D[i+1,j-1]-D[i,j-1] print(“Difference table”) for i in range(n): print(D[i,:n-i]) xp=3.5 h=x[1]-x[0] p=(xp-x[0])/h yp=y[0] prod=1 for i in range(1,n): prod=prod*p-(i-1)/i yp+= prod*D[0,i] print(“The value of Yp is”,yp)
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