Boundary Value Problems/Problem Lookup

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A directory/database of BVP problems.

PDE	BCs	ICs	Click for link to solution
1	2	3	4
$u_{xx}=\frac{1}{k}{u}_t$	$u(0,t)=0u(L,t)=0$	$u(x,0)=f(x)$	BVP_1D_heat_hom_dirichlet_hom
$u_{xx}=\frac{1}{k}{u}_t$	$u(0,t)=T_{1}u(L,t)=T_2$	$u(x,0)=f(x)$	BVP_1D_heat_hom_dirichlet_non_hom
$u_{xx}=\frac{1}{k}{u}_t$	$u_x(0,t)=0u(L,t)=T_1$	$u(x,0)=f(x)$	BVP_1D_heat_hom_neumann_dirichlet
$u_{xx}=\frac{1}{k}{u}_t$	$u_x(0,t)=-k(u(0,t)-A)u(L,t)=T_2$	$u(x,0)=f(x)$	BVP_1D_heat_hom_dirichlet_non_hom
$u_{xx}+g(x)=\frac{1}{k}{u}_t$	$u(0,t)=T_{1}u(L,t)=T_2$	$u(x,0)=f(x)$	BVP_1D_heat_hom_dirichlet_non_hom
$u_{xx}=\frac{1}{k}{u}_t+k(u(x,t)-A)$	$u(0,t)=T_{1}u(L,t)=T_2$	$u(x,0)=f(x)$	BVP_1D_heat_nonhom_dirichlet_non_hom
$u_{xx}=\frac{1}{k}{u}_t$	$u(0,t)=T_{1}u(L,t)=T_2$	$u(x,0)=f(x)$	BVP_2D_Laplaces_hom_BCs_non_hom
${\mathrm{\nabla }}^{2}u=0$	$u(0,y)=\pi -y$ $u(1,x)=0$ $u_y(x,0)=x$ $u_y(x,\pi )=x$	none	File:BVP 2D Laplaces nonh BCs nonh.pdf click here to see pdf of Maple file that has solution.
$u_{xx}=u_{tt}+10$	$u(0,t)=0$ $u(1,t)=0$	$u(x,0)=0$ $u_t(x,0)=x(1-x)$	File:Bvp 1d wave nonh bcs hom.pdf Click here to see pdf of a Maple file that has solution.
${\mathrm{\nabla }}^{2}u=\frac{1}{4}{u}_t$	$u(x,0,t)=0$ $u(x,5,t)=0$ $u(0,y,t)=0$ $u(3,y,t)=0$	$u(x,y,t)=sin(\frac{\pi x}{3})sin(\frac{\pi y}{5})$	File:BVP 2D heat homogeneous.pdf.pdf click here to see pdf of Maple file that has solution.
${\mathrm{\nabla }}^{2}u=\frac{1}{4}{u}_t$+ F(x,y,t)	$u(x,0,t)=0$ $u(x,M,t)=0$ $u(0,y,t)=0$ $u(L,y,t)=0$	$u(x,y,t)=sin(\frac{\pi x}{L})sin(\frac{\pi y}{M})$