Second Order of Accuracy Stable Difference Schemes for Hyperbolic Problems Subject to Nonlocal Conditions with Self-Adjoint Operator (original) (raw)

Nucleation and Atmospheric Aerosols, 2011

Abstract

In the present paper, two new second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value problemd2u(t)dt2+Au(t) = f(t) (0<=t<=1),u(0) = j = 1nalphaju(lambdaj)+J,ut(0) = j = 1nbetajut(lambdaj)+psi,0<lambda1<lambda2<...<lambdan<=1 for differential equations in a Hilbert space H with the self-adjoint positive definite operator A. The stability estimates for the solutions of these difference schemes are established.

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