Numerical approximation of boundary-value problems

Abstract

Boundary-value problems are differential problems set in an interval (a, b) of the real line or in an open multidimensional region Ω⊂ℝd(d=2,3)Ω⊂Rd(d=2,3)\it\Omega\subset\mathbb{R}^d(d=\mathrm{2,3}) for which the value of the unknown solution (or its derivatives) is prescribed at the end-points a and b of the interval, or on the boundary ∂Ω∂Ω\partial\it\Omega of the multidimensional region.