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Crank–Nicolson Method for the Advection-Diffusion Equation Involving a Fractional Laplace Operator

Author

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  • Martin Nitiema
  • Thomas Tindano
  • Windjiré Some

Abstract

We consider an advection-diffusion equation involving a fractional Laplace operator of order s∈]0;1]∖1/2. Using a combination of fractional left and right Riemann–Liouville derivatives of order 2s to approximate the fractional Laplace operator, we construct a numerical scheme using the Crank–Nicolson method. Using the Crank–Nicolson scheme, we succeeded in putting the numerical scheme of the problem under consideration in the form of a strictly and diagonally dominant positive definite matrix. This has allowed us to prove that the numerical scheme is stable and converges to first order in time and space for s∈]0;1]∖1/2. Numerical tests are performed to illustrate the results.MSC2020 Classification: 35R11; 35S15; 65M12.

Suggested Citation

  • Martin Nitiema & Thomas Tindano & Windjiré Some, 2025. "Crank–Nicolson Method for the Advection-Diffusion Equation Involving a Fractional Laplace Operator," Abstract and Applied Analysis, Hindawi, vol. 2025, pages 1-17, December.
    • Handle: RePEc:hin:jnlaaa:6642234
    DOI: 10.1155/aaa/6642234
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