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Two-level implicit high-order compact scheme in exponential form for 3D quasi-linear parabolic equations

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  • Mittal, Kajal
  • Ray, Rajendra K.

Abstract

We discuss a new high accuracy compact exponential scheme of order four in space and two in time to solve the three-dimensional quasi-linear parabolic partial differential equations. The derived half-step discretization based scheme is implicit in nature and demands only two levels for computation. The generalization of the proposed exponential scheme for the system of the quasi-linear parabolic PDEs is also represented. We generate unconditionally stable alternating direction implicit scheme for the linear parabolic equation in general form. The accuracy and the theoretical results of the proposed scheme are verified for high Reynolds number by several numerical problems like linear and non-linear convection-diffusion equation, coupled Burgers' equations, Navier-Stokes equations, quasi-linear parabolic equation, etc.

Suggested Citation

  • Mittal, Kajal & Ray, Rajendra K., 2025. "Two-level implicit high-order compact scheme in exponential form for 3D quasi-linear parabolic equations," Applied Mathematics and Computation, Elsevier, vol. 485(C).
    • Handle: RePEc:eee:apmaco:v:485:y:2025:i:c:s0096300324004454
    DOI: 10.1016/j.amc.2024.128984
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    References listed on IDEAS

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    1. Zhang, Jun & Ge, Lixin & Kouatchou, Jules, 2000. "A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 65-80.
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