A propositionalization of a theory in First-Order Logic (FOL) is a set of propositional sentences that is satisfiable iff the original theory is satisfiable. We cannot translate arbitrary FOL theories to propositional logic because FOL is only semi-decidable. However, when possible, it is often advantageous to do so because we can use optimized, efficient SAT solvers (e.g. [Moskewicz et al., 20...

In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients res...

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

Due to the wide application of Delaware nozzle in many fields, flow characteristics subsonic-supersonic isentropic De-Laval are analyzed numerically. The can be simplified a quasi-one-dimensional problem. First, MacCormack format is employed discretize control equations conservative form. Then, results with and without artificial viscosity compared. Grid independence also discussed. show that n...