### AIMS Mathematics

2022, Issue 5: 9172-9188. doi: 10.3934/math.2022508
Research article Special Issues

# High order compact difference scheme for solving the time multi-term fractional sub-diffusion equations

• Received: 28 December 2021 Revised: 18 February 2022 Accepted: 24 February 2022 Published: 09 March 2022
• MSC : 65M06, 65M12, 65M15, 35R11

• In this paper, a high order compact finite difference is established for the time multi-term fractional sub-diffusion equation. The derived numerical differential formula can achieve second order accuracy in time and four order accuracy in space. A unconditionally stable and convergent difference scheme is presented, and a rigorous proof for the stability and convergence is given. Numerical results demonstrate the efficiency of the proposed difference schemes.

Citation: Lei Ren. High order compact difference scheme for solving the time multi-term fractional sub-diffusion equations[J]. AIMS Mathematics, 2022, 7(5): 9172-9188. doi: 10.3934/math.2022508

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• In this paper, a high order compact finite difference is established for the time multi-term fractional sub-diffusion equation. The derived numerical differential formula can achieve second order accuracy in time and four order accuracy in space. A unconditionally stable and convergent difference scheme is presented, and a rigorous proof for the stability and convergence is given. Numerical results demonstrate the efficiency of the proposed difference schemes.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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