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A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x' and its two ends are embedded in ice at temperature zero. Consider the partial differential equation where: u, (x,t) = 5u „ (x,t), for 0 0 with the initial condition: u(x,0) = f(x) = 2x³ for 0

A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x' and its two ends are embedded in ice at temperature zero. Consider the partial differential equation where: u, (x,t) = 5u „ (x,t), for 0 0 with the initial condition: u(x,0) = f(x) = 2x³ for 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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A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x and its two ends are embedded in ice at temperature zero. Consider the partial differential equation where: u, (x,t) = 5u (x,1), for 0<x<1, t > 0 with the initial condition: u(x,0) = f(x) = 2x° for 0<x<1 and the boundary conditions: u(0,t) = 0, for 0st<0.10 u(1,t) = 2, for 0s150.10 (a) Show whether the partial differential equation is hyperbolic, parabolic or elliptic. (b) Describe graphically and explain how four points are used to generate the finite difference formula for heat equation. (c) Solve u(x,t) numerically with h= 0.2 and k =0.05.
Transcribed Image Text:A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x and its two ends are embedded in ice at temperature zero. Consider the partial differential equation where: u, (x,t) = 5u (x,1), for 0<x<1, t > 0 with the initial condition: u(x,0) = f(x) = 2x° for 0<x<1 and the boundary conditions: u(0,t) = 0, for 0st<0.10 u(1,t) = 2, for 0s150.10 (a) Show whether the partial differential equation is hyperbolic, parabolic or elliptic. (b) Describe graphically and explain how four points are used to generate the finite difference formula for heat equation. (c) Solve u(x,t) numerically with h= 0.2 and k =0.05.
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