We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. The model was recently introduced in [12] where existence of weak solutions was proved in three space dimensions. Here, we aim at studying the properties of solutions in the two-dimensional case. In particular, we can show existence of global in tim...

Recently, the Runge-Kutta methods, obtained via Taylor’s expansion is exist in the literature. In this study, we have derived explicit methods for problems of the form y′ = f(y) including second and third derivatives , by considering available Two-Derivative Runge-Kutta methods (TDRK). The methods use one evaluation of first derivative, one evaluation of second derivative and many evaluations o...

A formal two-phase model of democratic policy deliberation is presented, in which in the first phase sufficient and necessary criteria for proposals to be accepted are determined (the ‘admissible’ criteria’) and in the second phase proposals are made and evaluated in light of the admissible criteria resulting from the first phase. Argument schemes for both phases are defined and formalised in a...

We propose a new class of rigorous methods for derivative-free optimization with the aim delivering efficient and robust numerical performance functions all types, from smooth to non-smooth, under different noise regimes. To this end, we have developed methods, called Full-Low Evaluation organized around two main types iterations. The first iteration type (called Full-Eval) is expensive in func...