# Interval boundary element method

Interval boundary element method is classical boundary element method with the interval parameters.
Boundary element method is based on the following integral equation This article needs attention from an expert in mathematics. (February 2009)

${displaystyle ccdot u=int limits _{partial Omega }left(G{frac {partial u}{partial n}}-{frac {partial G}{partial n}}uright)dS}$ The exact interval solution on the boundary can be defined in the following way:

${displaystyle {tilde {u}}(x)={u(x,p):c(p)cdot u(p)=int limits _{partial Omega }left(G(p){frac {partial u(p)}{partial n}}-{frac {partial G(p)}{partial n}}u(p)right)dS,pin {hat {p}}}}$ In practice we are interested in the smallest interval which contain the exact solution set

${displaystyle {hat {u}}(x)=hull {tilde {u}}(x)=hull{u(x,p):c(p)cdot u(p)=int limits _{partial Omega }left(G(p){frac {partial u(p)}{partial n}}-{frac {partial G(p)}{partial n}}u(p)right)dS,pin {hat {p}}}}$ In similar way it is possible to calculate the interval solution inside the boundary

${displaystyle Omega }$

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## . . . Interval boundary element method . . .

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