In this paper,three kinds of discrete formulae for the Caputo fractional derivative are studied,including the modified L1 discretisation forα∈(O,1),and L2 discretisation and L2C discretisation forα∈(1,2).The trunc...In this paper,three kinds of discrete formulae for the Caputo fractional derivative are studied,including the modified L1 discretisation forα∈(O,1),and L2 discretisation and L2C discretisation forα∈(1,2).The truncation error estimates and the properties of the coeffcients of all these discretisations are analysed in more detail.Finally,the theoretical analyses areverifiedby thenumerical examples.展开更多
文摘In this paper,three kinds of discrete formulae for the Caputo fractional derivative are studied,including the modified L1 discretisation forα∈(O,1),and L2 discretisation and L2C discretisation forα∈(1,2).The truncation error estimates and the properties of the coeffcients of all these discretisations are analysed in more detail.Finally,the theoretical analyses areverifiedby thenumerical examples.
