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1) Solve the following initial value problem for u(t,x): ди ²u at əx² Satisfying the boundary and initial conditions ди əx u is ok as x→ ∞0&t> 0 u= 0 at t=0&x>0. = = 1 at x = 0 &t> 0 Is this solution uniformly convergent?

1) Solve the following initial value problem for u(t,x): ди ²u at əx² Satisfying the boundary and initial conditions ди əx u is ok as x→ ∞0&t> 0 u= 0 at t=0&x>0. = = 1 at x = 0 &t> 0 Is this solution uniformly convergent?

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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(d) Solve the following initial value problem for u(t,x): du ди ²u at əx² Satisfying the boundary and initial conditions ди == əx u is ok as x→∞&t> 0 = = 1 at x = 0 &t> 0 u = 0 at t = 0 & x > 0. Is this solution uniformly convergent?
Transcribed Image Text:(d) Solve the following initial value problem for u(t,x): du ди ²u at əx² Satisfying the boundary and initial conditions ди == əx u is ok as x→∞&t> 0 = = 1 at x = 0 &t> 0 u = 0 at t = 0 & x > 0. Is this solution uniformly convergent?
4. Consider an eigenvalue problem -u" - λu = 0; u ES = C₂ (0, ∞) and VvE S, v'(0) = 0 & v(x) = ok.
Transcribed Image Text:4. Consider an eigenvalue problem -u" - λu = 0; u ES = C₂ (0, ∞) and VvE S, v'(0) = 0 & v(x) = ok.
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