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Mathematics of Computation

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Sharp convergence rates for nonlinear product formulas

Author: Eric Schechter
Journal: Math. Comp. 43 (1984), 135-155
MSC: Primary 65J15; Secondary 34G20, 47H15
MathSciNet review: 744928
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Abstract: Nonlinear versions of the Lie-Trotter product formula $ \exp [t(A + B)] = {\lim _{n \to \infty }}{[\exp ((t/n)A)\exp ((t/n)B)]^n}$ and related formulas are given in this paper. The convergence rates are optimal. The results are applicable to some nonlinear partial differential equations.

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Keywords: Accretive, alternating direction method, approximation scheme, composition, convergence rate, dissipative, evolution, exponential, fractional step method, resolvent, semigroup, split step method
Article copyright: © Copyright 1984 American Mathematical Society

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