Orthogonal spline collocation scheme for the multi-term time-fractional diffusion equation

ABSTRACT

A novel numerical technique is considered for the solution of a multi-term time-fractional diffusion equation. The orthogonal spline collocation method is used for in space, and a finite difference method in time. The stability and convergence are provided. The numerical experiments for one and two dimensional problems support our theoretical analysis.

KEYWORDS:

• Multi-term time-fractional diffusion equation
• orthogonal spline collocation method
• stability
• convergence rates
• numerical experiments

CLASSIFICATION:

• 35R11
• 35R09
• 65M12

Acknowledgments

I am grateful to the referees for many helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The project supported by Hunan Provincial Innovation Foundation For Postgraduate, National Natural Science Foundation of China [grant number 11671131], Construct Program of the Key Discipline in Hunan Province, and a Scientific Research Fund of Hunan Provincial Education Department [16C0951].