The 2D Heat Equation on a Disk;

Homogeneous Dirichlet Boundary Conditions


exp(-k0,12 t) J0(k0,1 r)
k0,1 = 2.404825558...

exp(-k0,22 t) J0(k0,2 r)
k0,2 = 5.520078110...

exp(-k0,32 t) J0(k0,3 r)
k0,3 = 8.653727913...

exp(-k1,12 t) J1(k1,1 r) cos(θ)
k1,1 = 3.831705970...

exp(-k1,22 t) J1(k1,2 r) cos(θ)
k1,2 = 7.015586670...

exp(-k1,32 t) J1(k1,3 r) cos(θ)
k1,3 = 10.17346814...

exp(-k2,12 t) J2(k2,1 r) cos(2θ)
k2,1 = 5.135622302...

exp(-k2,22 t) J2(k2,2 r) cos(2θ)
k2,2 = 8.417244140...

exp(-k2,32 t) J2(k2,3 r) cos(2θ)
k2,3 = 11.61984117...

exp(-k3,12 t) J3(k3,1 r) cos(3θ)
k3,1 = 6.380161896...

exp(-k3,22 t) J3(k3,2 r) cos(3θ)
k3,2 = 9.761023130...

exp(-k3,32 t) J3(k3,3 r) cos(3θ)
k3,3 = 13.01520072...

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