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(1) u(x +h, t + k) + u(x - h, t – k) = u(x+ k, t+ h) + u(x – k,t – h), 2) Consider the initial boundary value problems: Ofu – u = 0, x E (0, T), t> 0, u(x, 0) = 0, dru(x, 0) = 1, x € (0, 7), initial data, %3D u(0, t) = 0, u(T, t) = 0, t > 0, boundary values. %3D %3D (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C' i.e, u(x, t) differentiable with du(x, t), du(a, t) continuous?

(1) u(x +h, t + k) + u(x - h, t – k) = u(x+ k, t+ h) + u(x – k,t – h), 2) Consider the initial boundary value problems: Ofu – u = 0, x E (0, T), t> 0, u(x, 0) = 0, dru(x, 0) = 1, x € (0, 7), initial data, %3D u(0, t) = 0, u(T, t) = 0, t > 0, boundary values. %3D %3D (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C' i.e, u(x, t) differentiable with du(x, t), du(a, t) continuous?

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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Subject :PARTIAL DIFFERENTIAL EQUATIONS kindly solve both Parts(a) & (b) as soon as possible. THANK-YOU!!
(1) u(x +h, t + k) + u(x - h, t- k) = u(x+ k, t+ h) + u(x – k,t – h), 2) Consider the initial boundary value problems: x E (0, T), t> 0, dru(x, 0) = 1, Ofu – u = 0, u(x, 0) = 0, x € (0, 7), initial data, %3D u(0, t) = 0, u(T, t) = 0, t > 0, boundary values. %3D %3D (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C' i.e, u(x, t) differentiable with du(x, t), d„u(x, t) continuous?
Transcribed Image Text:(1) u(x +h, t + k) + u(x - h, t- k) = u(x+ k, t+ h) + u(x – k,t – h), 2) Consider the initial boundary value problems: x E (0, T), t> 0, dru(x, 0) = 1, Ofu – u = 0, u(x, 0) = 0, x € (0, 7), initial data, %3D u(0, t) = 0, u(T, t) = 0, t > 0, boundary values. %3D %3D (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C' i.e, u(x, t) differentiable with du(x, t), d„u(x, t) continuous?
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