Overview of Boundary Value Applications

In a Nut Shell: The figures below display the two common types of homogeneous

boundary conditions for each application.

u(0,t) = 0 and u(L,t) = 0 specified temperatures at ends of thin rod

u_x(0,t) = 0 and u_x(L,t) = 0 ends of rod are insulated

u(0,t) = 0 and u(L,t) = 0 specified displacements at each end

u_x(0,t) = 0 and u_x(L,t) = 0 specified gradient of displacement at each end

u(0,t) = 0 and u(a,t) = 0 specified temperatures at ends of thin plate

u_x(0,t) = 0 and u_x(a,t) = 0 ends of thin plate are insulated

Click here for impact of boundary conditions on related eigenvalues and eigenvectors.

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