# 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

${displaystyle ccdot u=int limits _{partial Omega }left(G{frac {partial u}{partial n}}-{frac {partial G}{partial n}}uright)dS}$

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

${displaystyle Omega }$.

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

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

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