This paper presents a new 4-points Explicit Group Unsymmetric Successive Overrelaxation (USSOR) iterative method to approximate the solution of the linear systems derived from the discretisation of self-adjoint elliptic partial equations. Several studies have been carried out by many researchers on the USSOR iterative method, for example, the analysis of its convergence [1], an upper bound for ...

We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present st...

The synthesis of 1,4-diamines containing the (Z)-1,4-diaminobut-2-ene subunit via a temporary phosphorus tether/RCM strategy is described. We have developed a new method utilizing phosphorus nuclei as suitable temporary tethers for the coupling of nonracemic allylic amines. This approach allows for the generation of C(2)-symmetric and unsymmetric 1,4-diamines 1-3, which may have considerable sy...

The completely N1-selective Pd-catalyzed arylation of unsymmetric imidazoles with aryl halides and triflates is described. This study showed that imidazoles have a strong inhibitory effect on the in situ formation of catalytically-active Pd(0)-ligand complex. The efficacy of the N-arylation reaction was improved drastically by the use of pre-activated solution of Pd2(dba)3 and L1. From these fi...

In this paper we consider a direct method to solve a sparse unsymmetric system of linear equations Ax = b, which is the Gaussian elimination. This elimination consists in explicitly factoring the matrix A into the product of L and U , where L is a unit lower triangular matrix, and U is an upper triangular matrix, followed by solving LUx = b one factor at a time. One of the main characteristics ...

The paper studies multigrid methods for solving systems of linear algebraic equations resulting from the seven-point discretization three-dimensional Dirichlet problem an elliptic differential equation second order in a parallepipedal domain on regular grid. algorithms suggested are presented as special iteration processes incomplete factorization Krylov subspaces with hierarchical recursive ve...

An 8-node quadrilateral plane element US-QUAD8 is developed for linear isotropic hardening material in the framework of updated Lagrangian unsymmetric finite formulation where B L matrix constructed by classical shape function, and R higher-order basis function global coordinate system. The present eliminates influence Jacobian elemental stiffness guarantees quadratic completeness displacement ...

There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at benefits overtesting by using more collocation conditions than number basis functions. Overtesting not only reduces problem size, but is also known to be necessary stability convergence widely used unsymmetric Kansa-type strong-form methods. We consider kernel-...

Abstract In this article, axisymmetric deformations of coupled functionally graded conical shells are studied. The analytical solution is presented by using the complex hypergeometric and Legendre polynomial series. results agree closely with reference for isotropic revolution. symbolic package Mathematica commands added to article help readers search particular solutions. detailed solutions tw...