An Accelerated Splitting-up Method for Parabolic Equations

We approximate the solution u of the Cauchy problem ∂ ∂t u(t, x) r f r. Under natural conditions on solvability in the Sobolev spaces W m p , we show that for any k > 1 one can approximate the solution u with an error of order δ k , by an appropriate combination of the solutions v r along a sequence of time discretization, where δ is proportional to the step size of the grid. This result is obtained by using the time change introduced in [7], together with Richardson's method and a power series expansion of the error of splitting-up approximations in terms of δ.