Canonical Euler splitting method for parabolic partial functional differential algebraic equations

A novel canonical Euler splitting method is presented for semilinear composite stiff parabolic partial functional differential algebraic equations with initial and Dirichlet bound-ary conditions. The original partial differential problems are transformed into the semi-discrete problems by spatial discretization, and then the canonical Euler splitting method is employed to solve the resulting semi-discrete problems. Under appropriate assumptions, the stability and convergence theories of this method are established. A series of numerical experiments are given to illustrate the effectiveness of this method and the correctness of theoretical results.Numerical results also demonstrate that the constructed method can significantly improve the calculation speed.(c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.