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Consider the following linear equation system. Calculate the solution for the system using the Gauss-Jacobi (Consider e= 0.01 iterative method and initial values ​​equal to zero

Consider the following linear equation system. Calculate the solution for the system using the Gauss-Jacobi (Consider e= 0.01 iterative method and initial values ​​equal to zero

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following linear equation system. Calculate the solution for the system using the Gauss-Jacobi

(Consider e= 0.01 iterative method and initial values ​​equal to zero).

5x, +x, + x3 = 5 Зx, + 4х, + х, %3D6 [3х, + 3х, + 6х, %3D 0
Transcribed Image Text:5x, +x, + x3 = 5 Зx, + 4х, + х, %3D6 [3х, + 3х, + 6х, %3D 0
Expert Solution
Step 1

We need to calculate the solution for the given system using the Gauss-Jacobi

let x1=x, x2=y, x3=z so system is

5x+y+z=53x+4y+z=63x+3y+6z=0

Gauss-Jacobi iterations formulas

xk+1=15(5-yk-zk)yk+1=14(6-3xk-zk)zk+1=16(0-3xk-3yk)

initial values x0=0, y0=0, z0=0

 

 

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