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January 22, 2026AIP AdvancesOpen Access

Numerical investigation of fractional-order advection–diffusion–reaction problems using an efficient B-spline scheme

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Authors

HHHassan Q. HassanBMBewar A. Mahmood

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Overview

Numerical scheme solves fractional-order advection-diffusion-reaction equations, indicating high accuracy and computational efficiency.

Key Points

  • The main aim is to develop an efficient numerical scheme for solving fractional-order advection-diffusion-reaction equations accurately.
  • Developed a cubic exponential B-spline collocation method for solving the fractional-order equation.
  • Time derivatives treated in the Caputo sense and discretized using the L1 formula.
  • Spatial derivatives approximated by cubic exponential B-spline functions.
  • Nonlinear terms managed via quasi-linearization and stability validated by von Neumann analysis.
  • Achieves second-order accuracy in the proposed scheme.
  • Demonstrates highly accurate results when compared to earlier studies.
  • Proves computationally efficient for solving complex fractional partial differential equations.

Cite This Study

Hassan et al. (2026) studied this question.

synapsesocial.com/papers/6971bdcf642b1836717e2682https://doi.org/10.1063/5.0305160
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