Time-step sequences for parabolic differential equations Original Research Article

The Euler forward difference method is used for the explicit time integration of stiff systems of ordinary differential equations which originate from spatial discretization of parabolic partial differential equations. A sequence of non-equidistant time steps is derived. It primarily depends on one positive parameter, which determines an upper bound for the distance between the analytical solution and the approximation at every discrete time level in case the Jacobian matrix is constant. Use is made of modified Chebyshev polynomials. The asymptotic rate of convergence of the method is derived and its applicability in case the Jacobian matrix is non-constant is demonstrated.