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Consider the following boundary value problem: y" + y +1 = 2y' + t², y(0) = 2, y(1) = 4. (i) By using suitable finite-difference approximations to the derivatives, derive the following equation. (1+h)y;-1 + (h² – 2)y; = h²(t} – 1) – (1 – h)y+1 (ii) Solve the above boundary value problem above with step size h = 0.2. %3D

Consider the following boundary value problem: y" + y +1 = 2y' + t², y(0) = 2, y(1) = 4. (i) By using suitable finite-difference approximations to the derivatives, derive the following equation. (1+h)y;-1 + (h² – 2)y; = h²(t} – 1) – (1 – h)y+1 (ii) Solve the above boundary value problem above with step size h = 0.2. %3D

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 boundary value problem: y" + y +1 = 2y' + t², y(0) = 2, y(1) = 4. (i) By using suitable finite-difference approximations to the derivatives, derive the following equation. (1+h)yi-1 + (h² – 2)y; = h° (tỉ – 1) – (1 – h)y;+1 (i) Solve the above boundary value problem above with step size h = 0.2. %3D
Transcribed Image Text:Consider the following boundary value problem: y" + y +1 = 2y' + t², y(0) = 2, y(1) = 4. (i) By using suitable finite-difference approximations to the derivatives, derive the following equation. (1+h)yi-1 + (h² – 2)y; = h° (tỉ – 1) – (1 – h)y;+1 (i) Solve the above boundary value problem above with step size h = 0.2. %3D
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