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<p>This article considers a class of nonlinear spatial fractional backward diffusion problems. Implicit integration factor (IIF) format is a highly competitive approach for solving nonlinear diffusion systems, which has considerable stability and robustness. Therefore, we extend it to solve the nonlinear backward diffusion system, which is called the backward implicit integration factor (BIIF) method. The stability and error analysis of BIIF are introduced. In order to improve the computational efficiency of implementing BIIF, we propose the ARA-BG fast solving algorithm, which combines the adaptive restarting shift-invert Arnoldi (ARA) algorithm and the BiCGSTAB (BG) algorithm. Numerical experiments show that the BIIF method can achieve more stable and ideal accuracy compared to the Crank-Nicolson method, and also verify that the proposed ARA-BG algorithm is the most competitive among all tested algorithms in terms of CPU.</p>

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A fast backward implicit integration factor scheme for nonlinear spatial fractional backward diffusion problems

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Huanyan Jian,
  • Ping Xiong,
  • Xiaomei Qu,
  • Tao Liu,
  • Wenrong Tan

摘要

This article considers a class of nonlinear spatial fractional backward diffusion problems. Implicit integration factor (IIF) format is a highly competitive approach for solving nonlinear diffusion systems, which has considerable stability and robustness. Therefore, we extend it to solve the nonlinear backward diffusion system, which is called the backward implicit integration factor (BIIF) method. The stability and error analysis of BIIF are introduced. In order to improve the computational efficiency of implementing BIIF, we propose the ARA-BG fast solving algorithm, which combines the adaptive restarting shift-invert Arnoldi (ARA) algorithm and the BiCGSTAB (BG) algorithm. Numerical experiments show that the BIIF method can achieve more stable and ideal accuracy compared to the Crank-Nicolson method, and also verify that the proposed ARA-BG algorithm is the most competitive among all tested algorithms in terms of CPU.