Unconditional stability of alternating difference schemes with variable time steplengthes for dispersive equation

Guo, Geyang; Lü, Shujuan; Liu, Bo

doi:10.1016/j.amc.2015.04.037

Cited by 8 publications

(4 citation statements)

References 15 publications

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“…It is evident that DDM II (16) has intrinsic parallelism. Schemes (9)- (11) and schemes (13)-(15) construct two domain decomposition methods (12) and (16), respectively. The corresponding algorithm can be described as follows in Algorithm 1.…”

Section: Ddm IImentioning

confidence: 99%

“…The Alternating Segment Explicit-Implicit (ASE-I) scheme and the Alternating Segment Crank-Nicolson (ASC-N) scheme were designed in [4][5][6]. Afterwards, the alternating segment algorithms (AGE scheme, ASE-I scheme, and ASC-N scheme) above became very effective methods for some parabolic equations, such as heat equation [7], convection-diffusion equation [8][9][10], dispersive equation [11][12][13][14][15][16], forth-order parabolic equation [17][18][19]. Meanwhile, domain decomposition methods (DDMs) for the partial differential equations have been studied extensively [20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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A new parallel algorithm for solving parabolic equations

Xue

Feng

2018

Adv Differ Equ

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In this paper, a new parallel algorithm for solving parabolic equations is proposed. The new algorithm includes two domain decomposition methods, each method is applied to compute the values at (n + 1)st time level by use of known numerical solutions at nth time level, respectively. Then the average of two above values is chosen to be the numerical solutions at (n + 1)st time level. The new algorithm obtains satisfactory accuracy while maintaining parallelism and unconditional stability. This algorithm can be extended to solve two-dimensional parabolic equations by alternating direction implicit (ADI) technique. Both error analysis and numerical experiments illustrate the accuracy and efficiency of the new algorithm.

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Section: Ddm IImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new parallel algorithm for solving parabolic equations

Xue

Feng

2018

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

“…e Alternating Segment Crank-Nicolson (ASC-N) scheme was designed in [3]. Afterwards, the alternating segment algorithms (AGE scheme and ASC-N scheme) above became very effective methods for parabolic equations, such as convection-diffusion equation [4], dispersive equation [5][6][7][8], and fourth-order parabolic equation [9,10]. Meanwhile, domain decomposition methods (DDMs) for the partial differential equations have been developed.…”

Section: Introductionmentioning

confidence: 99%

The Splitting Crank–Nicolson Scheme with Intrinsic Parallelism for Solving Parabolic Equations

Xue

Gong

Feng

2020

Journal of Function Spaces

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In this paper, a splitting Crank–Nicolson (SC-N) scheme with intrinsic parallelism is proposed for parabolic equations. The new algorithm splits the Crank–Nicolson scheme into two domain decomposition methods, each one is applied to compute the values at (n + 1)th time level by use of known numerical solutions at n-th time level, respectively. Then, the average of the above two values is chosen to be the numerical solutions at (n + 1)th time level. The new algorithm obtains accuracy of the Crank–Nicolson scheme while maintaining parallelism and unconditional stability. This algorithm can be extended to solve two-dimensional parabolic equations by alternating direction implicit (ADI) technique. Numerical experiments illustrate the accuracy and efficiency of the new algorithm.

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“…Yuan et al [20] proposed a class of parallel difference schemes with 2-order spatial accuracy and unconditional stability for the nonlinear parabolic system. Guo et al [21] studied the difference method with intrinsic parallelism for the dispersive equation. e general alternating difference schemes with variable time steps are constructed and proved to be unconditionally stable.…”

Section: Introductionmentioning

confidence: 99%

A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation

Pan

Yang

2020

Mathematical Problems in Engineering

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This paper proposes a new class of difference methods with intrinsic parallelism for solving the Burgers–Fisher equation. A new class of parallel difference schemes of pure alternating segment explicit-implicit (PASE-I) and pure alternating segment implicit-explicit (PASI-E) are constructed by taking simple classical explicit and implicit schemes, combined with the alternating segment technique. The existence, uniqueness, linear absolute stability, and convergence for the solutions of PASE-I and PASI-E schemes are well illustrated. Both theoretical analysis and numerical experiments show that PASE-I and PASI-E schemes are linearly absolute stable, with 2-order time accuracy and 2-order spatial accuracy. Compared with the implicit scheme and the Crank–Nicolson (C-N) scheme, the computational efficiency of the PASE-I (PASI-E) scheme is greatly improved. The PASE-I and PASI-E schemes have obvious parallel computing properties, which show that the difference methods with intrinsic parallelism in this paper are feasible to solve the Burgers–Fisher equation.

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Unconditional stability of alternating difference schemes with variable time steplengthes for dispersive equation

Cited by 8 publications

References 15 publications

A new parallel algorithm for solving parabolic equations

A new parallel algorithm for solving parabolic equations

The Splitting Crank–Nicolson Scheme with Intrinsic Parallelism for Solving Parabolic Equations

A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation

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