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Crank–Nicolson Method for Singularly Perturbed Unsteady Parabolic Problem With Multiple Boundary Turning Points

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  • Yimesgen Mehari Kebede
  • Awoke Andargie Tiruneh
  • Endalew Getnet Tsega
  • Ivan Giorgio

Abstract

In this paper, a numerical scheme for a time-dependent singularly perturbed parabolic convection–diffusion problem with boundary turning points is presented. The problem exhibits a left boundary layer in the spatial domain. We use the Crank–Nicolson method for temporal discretization and a nonstandard finite difference approach for spatial discretization on uniform meshes. Through rigorous error analysis, it has been shown that the scheme is stable and parameter-uniform convergence with a second-order accuracy in time and a first-order accuracy in space. Three model examples are provided to show the applicability of the scheme. It is shown that the numerical results are in agreement with the theoretical findings.

Suggested Citation

  • Yimesgen Mehari Kebede & Awoke Andargie Tiruneh & Endalew Getnet Tsega & Ivan Giorgio, 2024. "Crank–Nicolson Method for Singularly Perturbed Unsteady Parabolic Problem With Multiple Boundary Turning Points," Advances in Mathematical Physics, Hindawi, vol. 2024, pages 1-15, December.
    • Handle: RePEc:hin:jnlamp:4895771
    DOI: 10.1155/admp/4895771
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