4. If we use the center difference formula for y" Yi+1 y" (x₂) and the midpoint difference formula for y' y'(x₁): = = - 2yi + Yi-1 h² Yi+1 - Yi-1 2h to approximate the solution to the nonlinear BVP +0(h²) -+0(h²), y″ = −(y')² − y+lnx, 1 ≤ x ≤ 2, y(1) = 0, y (2) = ln 2. (a) Let h = 0.5, solve for Y₁, where Y₁ is the numerical approximation to the exact solution y₁ = y(x₁) = y (1.5). (b) Let h = 0.25, write out the three equations for Y₁, Y₂, and Y3. Do not need to solve the system.
4. If we use the center difference formula for y" Yi+1 y" (x₂) and the midpoint difference formula for y' y'(x₁): = = - 2yi + Yi-1 h² Yi+1 - Yi-1 2h to approximate the solution to the nonlinear BVP +0(h²) -+0(h²), y″ = −(y')² − y+lnx, 1 ≤ x ≤ 2, y(1) = 0, y (2) = ln 2. (a) Let h = 0.5, solve for Y₁, where Y₁ is the numerical approximation to the exact solution y₁ = y(x₁) = y (1.5). (b) Let h = 0.25, write out the three equations for Y₁, Y₂, and Y3. Do not need to solve the system.
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:4. If we use the center difference formula for y"
y" (x₁)
and the midpoint difference formula for y'
y'(x₁) =
to approximate the solution to the nonlinear BVP
Yi+12yi + Yi-1
h²
Yi+1 - Yi-1
2h
+0(h²)
+0(h²),
y" = −(y')² − y + lnx, 1 ≤ x ≤ 2, y(1) = 0,
-
y (2) = ln 2.
(a) Let h = 0.5, solve for Y₁, where Y₁ is the numerical approximation to the exact solution y₁ = y(x₁) =
y(1.5).
(b) Let h = 0.25, write out the three equations for Y₁, Y₂, and Y3. Do not need to solve the system.
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