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Extensive numerical results show that the MTI-SP method converges uniformly and optimally in space with exponential convergence rate if the solution is smooth, and uniformly in time with linear convergence rate at O for ε∈ 0,1] with τ time step size and optimally with quadratic convergence rate at O τ2) in the regime when either ε="O(1) or 0<ε≤τ.
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By the diagonal method there exists a subsequence of ({u_{n}}) that converges uniformly (u_{0}) on any ([frac{1}{3k},1-frac{1}{3k}]subseteq (0,1)), (kgeq1).
This method converges quickly.
Additional conditions are proposed to the boundary functions so that the differentiated series converges uniformly.
A sequence in C X) converges strictly if the sequence is uniformly bounded in the supremum norm and converges uniformly on compact subsets ofX.
In particular, this scheme converges uniformly for both continuous and discrete spectrum components.
The method converges to Pareto-optimal points.
Hence, series (31) converges uniformly.
functions, such that converges uniformly to on.
It follows that h n converges uniformly to a continuous function, since g n ′ converges uniformly.
Therefore, we can find a subsequence such that converges uniformly on, and converges uniformly on.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com