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A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative

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Abstract

This paper considers a high-order numerical method for a computed solution of multidimensional convection-diffusion-reaction equation with time-fractional derivative subjected to appropriate initial and boundary conditions. The stability and error estimates of the proposed numerical approach are analyzed using the \(L^{\infty }(0,T;L^{2})\)-norm. The theoretical study suggests that the new technique is unconditionally stable and temporal accurate with order O(τ2+α), where τ denotes the time step and 0 < α < 1. This result shows that the developed algorithm is faster and more efficient than a broad range of numerical techniques widely studied in the literature for the considered problem. Numerical experiments confirm the theory and they indicate that the proposed numerical scheme converges with accuracy O(τ2+α + h4), where h represents the space step.

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The author appreciates the valuable comments of anonymous referees which helped to improve the quality of this paper.

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  1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 90950, Riyadh, 11632, Saudi Arabia

    Eric Ngondiep

  2. Hydrological Research Centre, Institute for Geological and Mining Research, 4110, Yaounde, Cameroon

    Eric Ngondiep

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Ngondiep, E. A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative. Numer Algor 94, 681–700 (2023). https://doi.org/10.1007/s11075-023-01516-x

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