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...

We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups...

The numerical solution of the one-dimensional nonlinear Klein-Gordon equation on an unbounded domain is studied in this paper. Split local absorbing boundary (SLAB) conditions are obtained by the operator splitting method, then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several nume...

We present an explicit second-order-accurate Godunov finite difference method for the solution of the equations of solid mechanics in one, two, and three spatial dimensions. The solid mechanics equations are solved in nonconservation form, with the novel application of a diffusion-like correction to enforce the gauge condition that the deformation tensor be the gradient of a vector. Physically ...

the purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $delta$ and give some inclusion relations.