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Verification of Convergence Rates of Numerical Solutions for Parabolic Equations

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  • Darae Jeong
  • Yibao Li
  • Chaeyoung Lee
  • Junxiang Yang
  • Yongho Choi
  • Junseok Kim

Abstract

In this paper, we propose a verification method for the convergence rates of the numerical solutions for parabolic equations. Specifically, we consider the numerical convergence rates of the heat equation, the Allen–Cahn equation, and the Cahn–Hilliard equation. Convergence test results show that if we refine the spatial and temporal steps at the same time, then we have the second-order convergence rate for the second-order scheme. However, in the case of the first-order in time and the second-order in space scheme, we may have the first-order or the second-order convergence rates depending on starting spatial and temporal step sizes. Therefore, for a rigorous numerical convergence test, we need to perform the spatial and the temporal convergence tests separately.

Suggested Citation

  • Darae Jeong & Yibao Li & Chaeyoung Lee & Junxiang Yang & Yongho Choi & Junseok Kim, 2019. "Verification of Convergence Rates of Numerical Solutions for Parabolic Equations," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, June.
    • Handle: RePEc:hin:jnlmpe:8152136
    DOI: 10.1155/2019/8152136
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    Cited by:

    1. Çayan, Seda & Özhan, B. Burak & Sezer, Mehmet, 2022. "A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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