Implicit Euler approximations of the equations governing the porous flow of two imiscible incompressible fluids are shown to be the Euler–Lagrange equations of a convex function. Tools from convex analysis are then used to develop robust fully discrete algorithms for their numerical approximation. Existence and uniqueness of solutions control volume approximations are established.

In this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient te...

In this paper, we prove that ζ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in Γ(α),Γ(n),Γ(l) over the ring C, l>n>α≥0 nonnegative integers. We extend result does satisfy Γ,Γ′,Γ″ field complex numbers, which proved by Li and Ye [Li BQ, Z. Algebraic equations concerning Riemann zeta function Euler gamma function. Indiana Univ Math J. 201...

We introduce a new filter or sum acceleration method which is the complementary error function with a logarithmic argument. It was inspired by the large order asymptotics of the Euler and Vandeven accelerations, which we show are both proportional to the erfc function also. We also show the relationship between Vandeven’s filter, the Erfc-Log filter and the “lagged-Euler” method. The theory for...

The purpose of this paper is to give formulas and Recurrence relations for the Apostol-Euler numbers polynomials order with complex aid Euler operator partial derivatives generating function. Relations among these neqative integer order, beta-type rational functions, finite combinatorial sums, Stirling numbers, Lah are given. Finally, new classes modification exponential type splines constructed.

In this paper, we study the sum of iterates of the Euler function.