Spline-interpolation solution of Cauchy problem for a harmonic function in a simply connected ۳D domain

Here we construct an approximate spline-interpolation solution of the Cauchy problem for the Laplace equation. Our construction describes two different methods based on solution of integral equations. The first method involves singular integral equation, and the second one is based on solution of a Fredholm equation. We present the linear and the polynomial examples clarifying the construction approaches.

Keywords:

Cauchy problem , integral equation , holomorphic function , spline , approximate solution