AbstractWe develop an accurate approximation of the normalized hyperbolic
operator sine family generated by a strongly positive operator
A in a Banach space X which represents the solution operator for the elliptic boundary
value problem. The solution of the corresponding inhomogeneous boundary value problem is found
through the solution operator and the Green function. Starting with the Dunford —
Cauchy representation for the normalized hyperbolic operator sine family and for the
Green function, we then discretize the integrals involved by the exponentially convergent
Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits
a two-level parallelism with respect to both the computation of resolvents and the
treatment of different values of the spatial variable x ∈ [0, 1].
