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math.NA2022★ 21 cited
Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations
Shi Jin, Nana Liu, Yue Yu
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multisc…
math.NA2022★ 23 cited
Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations
Chengchao Zhao, Nan Liu, Yuheng Ma +1
In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is construct…