• Author / Uploaded
• Md Saidur Rahman Kohinoor

Citation preview

Course: Introductory of numerical analysis Syllabus: 1. Numerical Differentiation 2. Numerical Integration  Trapezoidal Rule  Simpson’s 1⁄3 Rule  Simpson’s 3⁄8 Rule  Weddle’s Rule 3. Picard’s Method 4. Runge-kutta Method 5. Spline Function  Linear Splines  Quadratic Splines 6. LU Decomposition

Theory:  Numerical Integration Formula Derive:

Now, derive your desire Rules (Trapezoidal, Simpsons, Weddle) by adding this content. :D

 Trapezoidal Rule:

 Simpson’s 1⁄3 Rule:

 Simpson’s 3⁄8 Rule:

 Weddle’s Rule:

  Runge-Kutta Method:

Now, if you want, add this Fourth Order formula. :D

 Picard’s Method:

Mathematical Problem: 1. Simpson + Trapezoidal + Weddle: Question-1: Evaluate:

𝜋 2

∫0 𝑒 𝑠𝑖𝑛𝑥 𝑑𝑥 By using Simpson’s 1/3 rule. [ Divide Six equal point] Solution:

𝜋 2

Given, ∫ 0

.’. n = 6 Applying Simpson’s 1/3 rule,

𝑒 𝑠𝑖𝑛𝑥 𝑑𝑥

Now, Compare with exact value…

Another Problem:

2. Picard’s:

Example 15(b)

3. Spline:

4. LU:  2x + 3y + 4z = 1 7x + 4y + 3z = 2 4x + 3y + z = 9  x + 5y + z = 21 2x + y + 3z = 20 3x + y + 4z = 26