A variable step size numerical method based on fractional type quadratures for linear integro-differential equations ?
In this work a discretization in time of variable step size of the convolution equation u ( t ) = ? 0 t ( t - s ) ? - 1 u ( s ) d s , based on a fractional type quadrature is studied. The convergence is directly proved thanks to a suitable representation of the error by means of Peano kernels. Practical illustrations showing the efficiency of our numerical scheme are provided.
variable step fractional quadratures fractional integrals