A method, called “the discrete variational method”, has been recently presented by Furihata and Matsuo for designing finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations (PDEs). In this paper the method is enhanced so that the derived schemes be highly accurate in space by introducing higher order spatial difference ope...

We use two parameters for functions whose second (q, ?)-derivatives are bounded in order to prove several recent extensions of the Ostrowski inequality and its companion inequalities on ?)-Hahn difference operator. Furthermore, we procure some q-integral continuous as special cases main results well these generalizations. Symmetry plays an essential role determining correct methods solve dynami...

some necessary and sufficient conditions are given for the existence of a g-positive (g-repositive) solution to adjointable operator equations $ax=c,axa^{left( astright) }=c$ and $axb=c$ over hilbert $c^{ast}$-modules, respectively. moreover, the expressions of these general g-positive (g-repositive) solutions are also derived. some of the findings of this paper extend some known results in the...