A linear differential equation is given below: y" + 2y' + y = 0 for 0 ≤ x ≤ 1 with two additional equations: y(0) = 0 y(1) = 1 (a) Write a finite difference formula for the given governing equation. Use central difference formula for the derivatives. (b) Divide the domain into 4 equal segments (elements) and apply the finite difference formula and the boundary conditions appropriately to write a system of equations for the nodes.
A linear differential equation is given below: y" + 2y' + y = 0 for 0 ≤ x ≤ 1 with two additional equations: y(0) = 0 y(1) = 1 (a) Write a finite difference formula for the given governing equation. Use central difference formula for the derivatives. (b) Divide the domain into 4 equal segments (elements) and apply the finite difference formula and the boundary conditions appropriately to write a system of equations for the nodes.
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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Transcribed Image Text:A linear differential equation is given below:
y" + 2y' + y = 0 for 0 ≤ x ≤ 1
with two additional equations:
y(0) = 0
y(1) = 1
(a) Write a finite difference formula for the given governing equation. Use central difference formula
for the derivatives.
(b) Divide the domain into 4 equal segments (elements) and apply the finite difference formula and
the boundary conditions appropriately to write a system of equations for the nodes.
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