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An improved product type oscillation test for partial difference equations

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  • Karpuz, Başak
  • Özsavaş, Büşra

Abstract

We present new oscillation tests for the PΔEau(m+1,n)+bu(m,n+1)−cu(m,n)+p(m,n)u(m−τ,n−σ)=0,m,n=0,1,⋯,where a, b, c ∈ (0, ∞) and τ, σ ∈ {0, 1, ⋅⋅⋅}, and {p(m, n)} ⊂ [0, ∞). Our main result improves some of the well-known results in the literature. We also present a numerical example, where all the previous results in the literature fail to deliver an answer.

Suggested Citation

  • Karpuz, Başak & Özsavaş, Büşra, 2021. "An improved product type oscillation test for partial difference equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    • Handle: RePEc:eee:apmaco:v:391:y:2021:i:c:s009630032030583x
    DOI: 10.1016/j.amc.2020.125629
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    References listed on IDEAS

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    1. Gilli, Manfred & Kellezi, Evis & Pauletto, Giorgio, 2002. "Solving finite difference schemes arising in trivariate option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1499-1515, August.
    2. G. Ladas & Ch. G. Philos & Y. G. Sficas, 1989. "Sharp conditions for the oscillation of delay difference equations," International Journal of Stochastic Analysis, Hindawi, vol. 2, pages 1-11, January.
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