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Published at December 10

A class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model

math.NA

cs.NA

35K58, 65L20, 65M06, 65M12

Released Date: December 10, 2024

Authors: Hong-lin Liao¹, Tao Tang², Xuping Wang¹, Tao Zhou³

Aff.: ¹Nanjing University of Aeronautics and Astronautics; ²Guangzhou Nanfang College; ³Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Arxiv: http://arxiv.org/pdf/2412.07321v1

Order	Stand-alone conditions		Coupling condition
Order	Implicit part	Explicit part	Coupling condition
1	$\mathbf{b}^{T}\mathbf{1}=1$	$\hat{\mathbf{b}}^{T}\mathbf{1}=1$	-
2	$\mathbf{b}^{T}\mathbf{c}=\tfrac{1}{2}$	$\hat{\mathbf{b}}^{T}\mathbf{c}=\tfrac{1}{2}$	-
3	$\mathbf{b}^{T}\mathbf{c}^{.2}=\tfrac{1}{3}$	$\hat{\mathbf{b}}^{T}\mathbf{c}^{.2}=\tfrac{1}{3}$
	$\mathbf{b}^{T}A\mathbf{c}=\tfrac{1}{6}$	$\hat{\mathbf{b}}^{T}\widehat{A}\mathbf{c}=\tfrac{1}{6}$	$\mathbf{b}^{T}\widehat{A}\mathbf{c}=\tfrac{1}{6},\;\hat{\mathbf{b}}^{T}A% \mathbf{c}=\tfrac{1}{6}$