Heat conduction in a thin circular ring is described by the following PDE U₁=Uzz for t≥ 0. with periodic boundary conditions in space (x € [0, 2π]): u(0, t) = u(2ñ, t), u₂(0, t) = u₂(2ñ, t), etc. Solve using separation of variables, (i.e. u(x, t) = X(x)T(t)). Find a general solution (i.e. for arbitraty initial condition u(x,0) = f(x)) and describe the asymptotic behavior of all solutions as t→ ∞. Provide a physical interpretation of this behavior. u(0, t) = u(2n, t) ux(0,t)=ux (2n, t) U₂ = Uxx

Heat conduction in a thin circular ring is described by the following PDE U₁=Uzz for t≥ 0. with periodic boundary conditions in space (x € [0, 2π]): u(0, t) = u(2ñ, t), u₂(0, t) = u₂(2ñ, t), etc. Solve using separation of variables, (i.e. u(x, t) = X(x)T(t)). Find a general solution (i.e. for arbitraty initial condition u(x,0) = f(x)) and describe the asymptotic behavior of all solutions as t→ ∞. Provide a physical interpretation of this behavior. u(0, t) = u(2n, t) ux(0,t)=ux (2n, t) U₂ = Uxx

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.

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