Abstract An algebraic proof is presented for the finite strong standard completeness of Involutive Uninorm Logic with Fixed Point ( $${{\mathbf {IUL}}^{fp}}$$ IUL fp ). It may provide a first step towards settling problem $${\mathbf {IUL}}$$ , pos...

A new conservative finite difference scheme is presented for an initial-boundary value problem of the general Rosenau-RLW equation. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable, and second-order convergent. Numerical examples show the efficiency of the scheme.