In this paper, numerical solutions of the nonlinear Burgers_ equation are obtained by a method based on collocation of quintic B-splines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by one test problem. The numerical results are found to be in good agreement with...

This paper deals with a finite element method involving Petrov-Galerkin method with cubic B-splines as basis functions and quintic B-splines as weight functions to solve a general fourth order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet type of boundary ...

In this short note, we present some decay estimates for nonlinear solutions of 3d quintic, cubic NLS, and 2d quintic NLS (nonlinear Schrödinger equations).

We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer’s quintic polynomials.

The development of autonomous robots for agricultural applications includes motion planning, fruit picking, and collision avoidance with surrounding environments, these become challenging tasks. For harvesting applications, robust control the manipulator is needed effective robot. Several combinations Proportional(P)- Integrative(I)- Derivative(D) controllers are modelled a simulation study was...

It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source cros...

By means of a new variational method we report a direct solution for quintic and cubic-quintic nonlinear 1D Gross-Pitaeskii equations (GPE) in a harmonic confined potential. We explore the influence of the quintic nonlinear term on the ideal 1D pure cigar-like shape model for attractive and repulsive atom-atom interaction in Bose-Einstein condensates (BEC). Also, we offer a closed analytical ex...

Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to satisfy an extension of the Picard-Fuchs differential equations associated to the mirror quintic. The Ooguri-Va...

Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to satisfy an extension of the Picard-Fuchs differential equations associated to the mirror quintic. The Ooguri-Va...