General solutions of a three-level partial difference equation

Cheng, Sui Sun; Lu, Yifeng

doi:10.1016/s0898-1221(99)00239-4

Cited by 9 publications

(2 citation statements)

References 7 publications

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“…Stability criteria have also been derived for such equations, which involves two-level (see [2]) as well as three-level processes (cf. [3]). Besides, the question of stability and asymptotic representation of solutions of such difference schemes are also of fundamental importance.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of the solutions of a discrete reaction‐diffusion equation

Medina

Cheng

2002

International Journal of Mathematics and Mathematical Sciences

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Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of the solutions of a discrete reaction‐diffusion equation

Medina

Cheng

2002

International Journal of Mathematics and Mathematical Sciences

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“…Since the study of partial difference equations is more complicate than the study of ordinary difference equations, this topic is not so popular. Nevertheless there are some investigations on solvability, stability and other topic related to the equations (see, e.g., previous studies [5][6][7][8][9][10][11][12][13][14][15] ). Many partial difference equations stem from some problems in combinatorics, discrete mathematics, and other related areas (see, e.g., previous studies [16][17][18] ).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behaviour of the solutions of systems of partial linear homogeneous and nonhomogeneous difference equations

2020

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In this paper we consider the following system of partial linear homogeneous difference equations: xsfalse(i+2,jfalse)+asxs+1false(i+1,j+1false)+bsxsfalse(i,j+2false)=0,s=1,2,...,n−1,xnfalse(i+2,jfalse)+anx1false(i+1,j+1false)+bnxnfalse(i,j+2false)=0 and the system of partial linear nonhomogeneous difference equations: ysfalse(i+2,jfalse)+asys+1false(i+1,j+1false)+bsysfalse(i,j+2false)=fsfalse(i,jfalse),s=1,2,...,n−1,ynfalse(i+2,jfalse)+any1false(i+1,j+1false)+bnynfalse(i,j+2false)=fnfalse(i,jfalse) where n=2,3,..., xsfalse(0,jfalse)=ϕsfalse(jfalse), j=2,3,..., xsfalse(1,jfalse)=ψsfalse(jfalse),1emj=1,2,... (resp. ysfalse(0,jfalse)=ϕsfalse(jfalse), j=2,3,..., ysfalse(1,jfalse)=ψsfalse(jfalse),1emj=1,2,...) for the first system (resp. for the second system); as, bs, are real constants; fs:double-struckN2→double-struckR are known functions; ϕsfalse(jfalse),ψsfalse(jfalse) are given sequences; and s=1,2,...,n and the domain of the solutions of the above systems are the sets Nm=false{false(i,jfalse),1emi+j=mfalse}, m=2,3,.... More precisely, we find conditions so that every solution of the first system converges to 0 as i→∞ uniformly with respect to j. Moreover, we study the asymptotic stability of the trivial solution of the first system. In addition, under some conditions on fs, we prove that every solution of the second system is bounded, and finally, we find conditions on fs so that every solution of the second system converges to 0 as i→∞ uniformly with respect to j.

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Monotonicity for Genuinely Multi-step Methods: Results and Issues From a Simple Lattice Boltzmann Scheme

Bellotti

2023

Springer Proceedings in Mathematics &Amp; Statistics

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General solutions of a three-level partial difference equation

Cited by 9 publications

References 7 publications

Asymptotic behavior of the solutions of a discrete reaction‐diffusion equation

Asymptotic behavior of the solutions of a discrete reaction‐diffusion equation

Asymptotic behaviour of the solutions of systems of partial linear homogeneous and nonhomogeneous difference equations

Monotonicity for Genuinely Multi-step Methods: Results and Issues From a Simple Lattice Boltzmann Scheme

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