High order fractional backward differentiation formulae

Abstract

For the fractional differential equation, we present a new kind of high order fractional backward differentiation formulae. The coefficients of this new scheme are obtained by using the order conditions and generating functions. The new scheme has two distinct features: (i) it can achieve the order in theory in numerical computations, and (ii) it is -stable.

Keywords:

• Fractional differential equation
• fractional linear multistep method
• backward differentiation formula
• stability

AMS Subject Classifications:

• 65L06
• 65L20

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11271102], [grant number 11671112].