In this paper, the multigrid algorithm was used to solve Poisson’s equation for various right-hand sides. However, in order to calculate the discretized laplacian value, both a second-order and a fourth-order laplacian operator was used. The fourth-order laplacian operator achieves higher accuracy at the cost of more calculations and a longer execution time. In order to compensate for this, the...

in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

We study the following third-order p-Laplacian m-point boundary value problems on time scales φp uΔ∇ ∇ a t f t, u t 0, t ∈ 0, T T , u 0 ∑m−2 i 1 biu ξi , u Δ T 0, φp uΔ∇ 0 ∑m−2 i 1 ciφp u Δ∇ ξi , where φp s is p-Laplacian operator, that is, φp s |s|p−2s, p > 1, φ−1 p φq, 1/p 1/q 1, 0 < ξ1 < · · · < ξm−2 < ρ T . We obtain the existence of positive solutions by using fixed-point theorem in cones....

for a simple connected graph $g$ with $n$-vertices having laplacian eigenvalues‎ ‎$mu_1$‎, ‎$mu_2$‎, ‎$dots$‎, ‎$mu_{n-1}$‎, ‎$mu_n=0$‎, ‎and signless laplacian eigenvalues $q_1‎, ‎q_2,dots‎, ‎q_n$‎, ‎the laplacian-energy-like invariant($lel$) and the incidence energy ($ie$) of a graph $g$ are respectively defined as $lel(g)=sum_{i=1}^{n-1}sqrt{mu_i}$ and $ie(g)=sum_{i=1}^{n}sqrt{q_i}$‎. ‎in th...

We propose a box and ball system with a periodic boundary condition (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent with the algorithm of the calculus for the 2Nth root. The relations to the pBBS of the combinatorial R matrix of U q(A (1) N ) are also discussed.

This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resultin...