Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Reduction rules for YAWL workflows with cancellation regions and OR-joins

As the need for concepts such as cancellation and OR-joins occurs naturally in business scenarios, comprehensive support in a workflow language is desirable. However, there is a clear trade-off between the expressive power of a language (i.e., introducing complex constructs such as cancellation and OR-joins) and ease of verification. When a workflow contains a large number of tasks and involves complex control flow dependencies, verification can take too much time or it may even be impossible. There are a number of different approaches to deal with this complexity. Reducing the size of the workflow, while preserving its essential properties with respect to a particular analysis problem, is one such approach. In this paper, we present a set of reduction rules for workflows with cancellation regions and OR-joins and demonstrate how they can be used to improve the efficiency of verification. Our results are presented in the context of the YAWL workflow language.