on the convergence of the generalized aor method abstract we consider the generalized aor method presented by k r james we give some convergence theorems for various kinds of matrices namely when the coefficient matrix of the linear system is positive definite an h l or m matrix or strictly or irreducibly diagonally dominant

igaor and multisplitting igaor methods for linear complementarity problems in this paper we propose an interval version of the generalized accelerated overrelaxation methods which we refer to as igaor for solving the linear complementarity problems lcp m q and develop a class of multisplitting igaor methods which can be easily implemented in parallel in addition in regards to the h matrix with positive diagonal elements we prove the convergence of these algorithms and illustrate their efficiency through our numerical results

positive solutions for one dimensional p laplacian boundary value problems with dependence on the first order derivative abstract this paper presents sufficient conditions for the existence and multiplicity of positive solutions to the one dimensional p laplacian differential equation p u a t f u u 0 subject to some boundary conditions we show that it has at least one or two or three positive solutions under some assumptions by applying the fixed point theorem

a rigid inclusion in an elastic space under the action of a uniform heat flow in the inclusion plane abstract a solution is presented for the three dimensional static thermoelastic problem of an absolutely rigid inclusion anticrack in the case when a uniform heat flow is directed along the inclusion plane by using the potential method and the fourier transform technique the problem is reduced to a system of coupled two dimensional singular integral equations for the shear stress jumps across the inclusion as an illustration a typical application to the circular anticrack is presented explicit expressions for the thermal stresses in the inclusion plane are obtained and discussed from the point of view of material failure

chaotic iterative methods for the linear complementarity problems a class of parallel multisplitting chaotic relaxation methods is established for the large sparse linear complementarity problems and the global and monotone convergence is proved for the h matrix and the l matrix classes respectively moreover comparison theorem is given which describes the influences of the parameters and the multiple splittings upon the monotone convergence rates of the new methods

convergence of gaor method for doubly diagonally dominant matrices abstract in this paper we obtain bounds for the spectral radius of the matrix l r which is the iterative matrix of the generalized accelerated overrelaxation gaor iterative method moreover we present one convergence theorem of the gaor method finally we present two numerical examples

bonded contact of a flexible elliptical disk with a transversely isotropic half space abstract the article concerns the problem of bonded contact of a thin flexible elliptical disk with a transversely isotropic half space three different cases of loading have been considered a the disk is loaded by a transverse force whose line of action passes through the center of the disk and lies in the plane of the disk b the disk is subjected to a rotation by a torque whose axis is perpendicular to the surface of the half space c the half space with the bonded disk is under uniform stress field at infinity the problem corresponding to all three cases is reduced in a unified manner to a set of coupled two dimensional integral equations closed form solutions for these equations have been obtained by using galins theorem

three positive solutions for the one dimensional p laplacian in this paper nonlinear two point boundary value problems with p laplacian operators subject to dirichlet boundary condition and nonlinear boundary conditions are studied we show the existence of three positive solutions by the five functionals fixed point theorem

generalized aor methods for linear complementarity problem abstract in this paper we firstly establish a class of generalized aor gaor methods for solving a linear complementarity problem lcp m q whose special case reduces to generalized sor gsor method then some sufficient conditions for convergence of the gaor and gsor methods are presented when the system matrix m is an h matrix m matrix and a strictly or irreducible diagonally dominant matrix moreover when m is an l matrix we discuss the monotone convergence of the new methods lastly we report some computational results with the proposed methods

existence of positive solutions for the one dimensional singular p laplacian this paper concerns the positive solutions of boundary value problems for the one dimensional singular p laplacian by the classical method of elliptic regularization we obtain some existence results which generalize some results of w zhou x wei positive solutions to bvps for a singular differential equation nonlinear anal 2006 doi 10 1016 j na 2006 06 015

existence theorems for the one dimensional singular p laplacian equation with sign changing nonlinearities in this paper general existence theorems are presented for the singular equation f p y f t y 0 y 0 y 1 0 throughout our nonlinearity is allowed to change sign

discontinuous viscosity solutions of a degenerate parabolic equation we study a nonlinear degenerate parabolic equation of the second order regularizing the equation by adding some artificial viscosity we construct a generalized solution we show that this solution is not necessarily continuous at all points

comparison of three classes of algorithms for the solution of the linear complementarity problem with an h matrix abstract there are three main classes of iterative methods for the solution of the linear complementarity problem lcp in order of appearance these classes are the projected iterative methods the block modulus algorithms and the modulus based matrix splitting iterative methods which of the three classes of methods is the best one to use for the solution of a certain problem is more or less an open question despite the fact that the best method within each class is known it is pointed out that by best we mean the minimal upper bound of the norm of the matrix operator of the absolute error vector at any iteration step with respect to the norm of the absolute initial error vector note that the first and the third classes of methods are iterative ones while the second one is iterative but needs outer n and unknown number of inner iteration steps to terminate one of the main objectives of this work is to consider the solution of the lcp with an h matrix and compare and decide theoretically if possible otherwise by numerical experiments as to which of the three best methods is the best one to use in practice

existence and uniqueness for a class of quasilinear elliptic boundary value problems abstract we prove existence and uniqueness of positive solutions for the boundary value problem r n 1 u r n 1 f u u 0 u 1 0 where x x p 2x f x xp 1 may not be decreasing on 0 and is a large parameter

multiple positive solutions for the one dimensional singular p laplacian we consider the following boundary value problem f p y q t f y 0 p 1 t 0 1 with y 0 y 1 0 or y 0 y 1 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem an example is also included to illustrate the importance of the result obtained

the normal shift of a rigid elliptical disk in a transversely isotropic solid abstract the paper addresses an elastostatic problem concerning an elliptical disk embedded in a transversely isotropic space the disk is assumed to be absolutely rigid and in perfect contact with the medium then the problem addressed consists of finding the elastic field in the medium when the disk is given a small shift along the direction perpendicular to its plane using the theory of two dimensional fourier transforms the problem is reduced to a two dimensional integral equation closed form solution to this equation is obtained by using ferrers dyson s and galin s theorems explicit expressions are deduced for the displacements and stresses in the entire plane of the disk closed form solution for the stress intensity factors near the edge of the disk is then extracted

modified aor methods for linear complementarity problem in order to solve a linear complementarity problem lcp m q when m is a 2 cyclic matrix a class of modified aor maor methods based on maor methods for solving linear system whose special case reduces modified sor msor method is proposed some sufficient conditions for convergence of the maor and msor methods are given when the system matrix m is an h matrix m matrix and a strictly or irreducible diagonally dominant matrix when m is an l matrix their monotone convergence are discussed

two class of synchronous matrix multisplitting schemes for solving linear complementarity problems many problems in the areas of scientific computing and engineering applications can lead to the solution of the linear complementarity problem lcp m q it is well known that the matrix multisplitting methods have been found very useful for solving lcp m q in this article by applying the generalized accelerated overrelaxation gaor and the symmetric successive overrelaxation ssor techniques we introduce two class of synchronous matrix multisplitting methods to solve lcp m q convergence results for these two methods are presented when m is an h matrix and also an m matrix also the monotone convergence of the new methods is established finally the numerical results show that the introduced methods are effective for solving the large and sparse linear complementary problems

the matrix analogue of the scalar aor iterative method the accelerated overrelaxation aor and the generalized aor gaor iterative methods for the solution of linear systems of algebraic equations a x b a c n i n det a 0 b c n have been around for about four decades and a plethora of variations of them have been proposed in this work a novel algorithm is introduced the matrix analogue of the aor maaor iterative method which is analysed and studied the maaor method generalizes both the aor and the gaor sufficient convergence conditions for the gaor method are determined when the coefficient matrix a of the linear system to be solved is a hermitian matrix with positive diagonal elements similarly sufficient convergence conditions for the maaor method are determined when a is a nonsingular h matrix the new convergence conditions are the most general ones so far numerical examples are presented in support of the theory developed

on convergence of two stage splitting methods for linear complementarity problems in this paper we study the splitting method and two stage splitting method for the linear complementarity problems convergence results for these two methods are presented when the system matrix is an h matrix and the splittings used are h splitting numerical experiments show that the two stage splitting method has the same or even better numerical performance than the splitting method in some aspects under certain conditions