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a) Solve the following PDE using an appropriate method. ²u ²u əx² at²' c². = 0 < x < 2, with BCs; u(0, t) = u(2,t) = 0 and IC; u(x,0)=2x-x² and ut(x,0) = x for 0 < x < 2 b) Derive an approximating finite difference equation for the following BVP using central differences in both time and space. ởu Au əx² at² c². = 0 < t < 00 with -∞0 < x <∞, 0

a) Solve the following PDE using an appropriate method. ²u ²u əx² at²' c². = 0 < x < 2, with BCs; u(0, t) = u(2,t) = 0 and IC; u(x,0)=2x-x² and ut(x,0) = x for 0 < x < 2 b) Derive an approximating finite difference equation for the following BVP using central differences in both time and space. ởu Au əx² at² c². = 0 < t < 00 with -∞0 < x <∞, 0

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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3. a) Solve the following PDE using an appropriate method. a²u 2²u əx² at², C2 = with BCs; u(0, t) = u(2,t) = 0 and IC; u(x,0) = 2x - x² and u(x, 0) = x for 0 < x < 2 0 < x < 2, b) Derive an approximating finite difference equation for the following BVP using central differences in both time and space. 2²u 2²u əx² at² c². with = 0 < t <∞0 7 -∞0 < x < 00, 0 < t < 00 ICS; u(x,0) = f(x) and ut(x,0) = g(x) for-c∞0 < x < 00
Transcribed Image Text:3. a) Solve the following PDE using an appropriate method. a²u 2²u əx² at², C2 = with BCs; u(0, t) = u(2,t) = 0 and IC; u(x,0) = 2x - x² and u(x, 0) = x for 0 < x < 2 0 < x < 2, b) Derive an approximating finite difference equation for the following BVP using central differences in both time and space. 2²u 2²u əx² at² c². with = 0 < t <∞0 7 -∞0 < x < 00, 0 < t < 00 ICS; u(x,0) = f(x) and ut(x,0) = g(x) for-c∞0 < x < 00
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