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This article contributes to this topic by proposing a novel class of <jats:italic>A<\/jats:italic> stable SBP time integration methods which can also be reformulated as implicit Runge-Kutta methods. In contrast to existing SBP time integration methods using simultaneous approximation terms to impose the initial condition weakly, the new schemes use a projection method to impose the initial condition strongly without destroying the SBP property. The new class of methods includes the classical Lobatto\u00a0IIIA collocation method, not previously formulated as an SBP scheme. 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