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b) Given a second order differential equation d'y 1 dy + d.x² x dx with boundary conditions. Y x² = 0, y(2) = 0.008, y (8) = 0.001. i. By using finite difference method, show that the difference equation for the prob- lem above can be written as h h [¹ - 2] -- [2 + ( ² ) ] × - [¹ + 2 ] Yi-1 2+ Yi + Yi+1 2xi 2xi = 0. = ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ay = b where h = 1.5. iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii). (DO NOT SOLVE the system)

b) Given a second order differential equation d'y 1 dy + d.x² x dx with boundary conditions. Y x² = 0, y(2) = 0.008, y (8) = 0.001. i. By using finite difference method, show that the difference equation for the prob- lem above can be written as h h [¹ - 2] -- [2 + ( ² ) ] × - [¹ + 2 ] Yi-1 2+ Yi + Yi+1 2xi 2xi = 0. = ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ay = b where h = 1.5. iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii). (DO NOT SOLVE the system)

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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b) Given a second order differential equation 1 dy x dx with boundary conditions d'y dx² + Y x² = 0, y (2) = 0.008, y(8) = 0.001. i. By using finite difference method, show that the difference equation for the prob- lem above can be written as h h [¹ – 2 ] × ₁ - [2 + ( 2 ) ] × + [¹ + 2 ] Yi-1 Yi 2x₂ 2xi Yi+1 = 0. = ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ay = b where h = 1.5. iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii). (DO NOT SOLVE the system)
Transcribed Image Text:b) Given a second order differential equation 1 dy x dx with boundary conditions d'y dx² + Y x² = 0, y (2) = 0.008, y(8) = 0.001. i. By using finite difference method, show that the difference equation for the prob- lem above can be written as h h [¹ – 2 ] × ₁ - [2 + ( 2 ) ] × + [¹ + 2 ] Yi-1 Yi 2x₂ 2xi Yi+1 = 0. = ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ay = b where h = 1.5. iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii). (DO NOT SOLVE the system)
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