Abstract This paper reviews strong stability preserving discrete variable methods for differential systems. The Runge–Kutta have been usually investigated in the literature on subject, using so-called Shu–Osher representation of these methods, as a convex combination first-order steps by forward Euler method. In this paper, we revisit analysis reformulating subclass general linear ordinary equa...

In this paper, concept of fuzzy continuous operator, bounded linear operator are introduced in strong [Formula: see text]-b-normed spaces and their relations studied. Idea norm is developed completeness BF(X,Y) established.

We have already seen how to take the dual of a linear program in general form. However, when we are solving a problem using linear programming, it can be very enlightening to take the dual of the linear program for that particular problem. Typically, in the context of the problem under study, it is possible to give a natural interpretation to the dual variables, and this also often leads to nat...

As we have seen before, using strong duality, we know that the optimum value for the following two linear programming are equal, i.e. u = w, if they are both feasible. u = max{cx : Ax ≤ b, x ≥ 0} (P ) w = min{b y : A y ≥ c, y ≥ 0} (D) Using the above result, we can check the optimality of a primal and/or a dual solution. Theorem 1. Suppose x and y are feasible solutions to (P ) and (D). Then x ...