Testwiki:Reference desk/Archives/Computing/2024 July 8

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July 8

Solving heat equation using Fourier series

Do "the boundary conditions u(0,t)=0=u(L,t)" imply the use of instrumentation or mechanics? As part of the solution to u(x,t), D_subscript_n was solved using integration. Afrazer123 (talk) 06:21, 8 July 2024 (UTC)

Boundary conditions would be a an assumption made to make a particular problem solvable and come up with a particular solution rather than just an equation. Perhaps you could assume that the value was measured at 0. But complete measurement time time=-infinity to +infinity will never happen. So you had better imagine it. Graeme Bartlett (talk) 06:55, 8 July 2024 (UTC)

These boundary conditions do not imply the use of either instrumentation or mechanics. They represent nothing but a simple special case for which the heat equation can be solved purely analytically, given also an initial condition of the form $u(x,0)=f(x),x\in [0,L].$  --Lambiam 10:29, 8 July 2024 (UTC)