Gavrilyuk, I. P.; Makarov, V. L.; Vasylyk, V. B.
October 2006
Computational Methods in Applied Mathematics;2006, Vol. 6 Issue 4, p386
Academic Journal
We develop an accurate approximation of the normalized hyperbolic operator sine family sinh-1(√A) sinh(x√A) generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem d²u/dx² - Au = 0, x ∈ (0, 1); u(0) = 0, u(1) = u1; u, u1 ∈ X. 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].


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