A stability preserved time-integration method for nonlinear advection-diffusion-reaction processes

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Tunc H., SARI M.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.59, sa.8, ss.1917-1937, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 8
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s10910-021-01271-1
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Chemical Abstracts Core, zbMATH
  • Sayfa Sayıları: ss.1917-1937
  • Anahtar Kelimeler: Chapman model, Advection-diffusion-reaction processes, Stability analysis, Taylor series, Time-integration, DISCONTINUOUS GALERKIN METHODS, SPECTRAL COLLOCATION METHOD, NUMERICAL-SOLUTION, TAYLOR-SERIES, STIFF SYSTEMS, BURGERS, IMPLEMENTATION, EQUATIONS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

A new implicit-explicit local differential transform method (IELDTM) is derived here for time integration of the nonlinear (2 + 1)-dimensional advection-diffusion-reaction (ADR) equations. The IELDTM is adaptively constructed as a stability preserved and high order time integrator for spatially discretized ADR equations. For spatial discretization of the model equation, the Chebyshev spectral collocation method (ChCM) is utilized. A robust stability analysis and global error analysis of the IELDTM are presented with respect to the direction parameter theta. With the help of the global error analysis, adaptivity equations are derived to minimize the computational costs of the algorithms. The produced method is shown to eliminate the accuracy disadvantage of the classical theta-method and the stability disadvantages of the existing differential transform-based methods. Two examples of the Burgers equation in one and two space dimensions and the Chapman oxygen-ozone ADR model are solved via the ChCM-IELDTM hybridization. The present time integrator is proven to provide more efficient numerical characteristics than the various multi-step and multi-stage time integration methods. The IELDTM is extensively compared with the widely used MATLAB solvers, ode45 and ode15s. The adaptive IELDTM has been proven to integrate the stiff Chapman ADR equations with optimum costs over relatively long-time intervals.