vibration analysis of arbitrarily shaped membranes using non dimensional dynamic influence function abstract in the present study a theoretical formulation based on the collocation method is presented for the vibration analysis of arbitrarily shaped membranes the mathematical relation between the two points of selected collocation points is given by a special function the so called non dimensional dynamic influence function unlike the collocation methods in the literature approximate functions used in this paper are simple one dimensional functions of which the only independent variable is the distance between the two points the function is also a wave type solution that satisfies exactly the given governing differential equation and physically describes the displacement reponse of a point in an infinite membrane due to a unit displacement excited at another point the approximate solution is obtained by linear superposition of non dimensional dynamic influence functions and then boundary conditions are applied at the discrete points the system matrix is always symmetric regardless of the boundary shape of the membrane and the calculated eigenvalues rapidly converge to the exact values thanks to the special function employed in this study moreover the method gives the associated mode shapes successfully without using interpolation functions between the boundary nodes the validity and efficiency of the method proposed in this paper are illustrated through several numerical examples

local radial basis function based gridfree scheme for unsteady incompressible viscous flows a local radial basic function rbf based gridfree scheme has been developed to solve unsteady incompressible navier stokes equations in primitive variables the velocity pressure decoupling is obtained by making use of a fractional step algorithm the scheme is validated over a variety of benchmark problems and found a very good agreement with the existing results comparisons with the benchmark solutions show that the developed local rbf gridfree scheme is stable and produces accurate results on domains discretized even with non uniform distribution of nodal points

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

hypersingular meshless method using double layer potentials for three dimensional exterior acoustic problems three dimensional exterior acoustic problems with irregular domains are solved using a hypersingular meshless method in particular the method of fundamental solutions mfs is used to formulate and analyze such acoustic problems it is well known that source points for mfs cannot be located on the real boundary due to the singularity of the kernel functions thus the diagonal terms of the influence matrices are unobtainable when source points are located on the boundary an efficient approach is proposed to overcome such difficulties when the mfs is used for three dimensional exterior acoustic problems this work is an extension of previous research on two dimensional problems the solution of the problem is expressed in terms of a double layer potential representation on the physical boundary three examples are presented in which the proposed method is compared to the mfs and boundary element method good numerical performance is demonstrated by the proposed hypersingular meshless method

a meshless method for solving an inverse spacewise dependent heat source problem in this paper an effective meshless and integration free numerical scheme for solving an inverse spacewise dependent heat source problem is proposed due to the use of the fundamental solution as basis functions the method leads to a global approximation scheme in both spatial and time domains the standard tikhonov regularization technique with the generalized cross validation criterion for choosing the regularization parameter is adopted for solving the resulting ill conditioned system of linear algebraic equations the effectiveness of the algorithm is illustrated by several numerical examples

solve partial differential equations by two or more radial basis functions abstract there are many partial differential equations their solution might be oscillatory or vary rapidly we will get an inaccurate result or encounter an ill conditioned problem whenever we solve it using kansa s collocation method mfs or other methods in this paper we will present a new method in which such pdes will be solved by two or more radial basis functions rbfs so these pdes can be solved efficiently and accurately

efficient algorithms for fuzzy qualitative temporal reasoning fuzzy qualitative temporal relations have been proposed to reason about events whose temporal boundaries are ill defined although the corresponding reasoning tasks are in the same complexity class as their crisp counterparts in practice the scalability of fuzzy temporal reasoners may be insufficient for applications that require a high expressivity and deal with a large number of events on the other hand transitivity rules can be used to make sound but incomplete inferences in polynomial time utilizing a variant of allen s path consistency algorithm the aim of this paper is to investigate how this polynomial time algorithm can be improved without altering its time complexity to this end we establish a characterization of 2 consistency of fuzzy temporal relations and provide transitivity rules that are significantly stronger than those resulting from straightforwardly generalizing transitivity rules for crisp temporal relations we furthermore provide experimental evidence for the effectiveness of our improved algorithm

a particular solution trefftz method for non linear poisson problems in heat and mass transfer this paper proposes a computational procedure based on the trefftz method for the solution of non linear poisson problems the problem is solved by finding an approximate particular solution to the poisson equation and using boundary collocation to solve the resulting laplace equation this method results in a global collocation and hence eliminates the need for discretization of the domain in both two and three dimensions the solution procedure proposed earlier in the literature based upon the above method has been reformulated for increased computational efficiency a quasi newton iteration method along with a new heuristic for source point location is used for efficient convergence of the numerical scheme the efficacy of the new formulation has been demonstrated for two classes of problems viz the thermal explosion problem and the diffusion reaction problem in a partially wetted catalyst pellet a brief error analysis of the method as well as future research directions is presented

numerical treatment of acoustic problems with boundary singularities by the singular boundary method abstract the singular boundary method sbm is a novel boundary type meshless method based on the fundamental solution of the given governing equation the sbm employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions in this paper we investigate the acoustic problems with boundary singularities using the sbm this is achieved by combining the sbm with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution the singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities then the regular solution is obtained by the sbm numerical examples show the excellent performance of the proposed technique

qualitative relations between moving objects in a network changing its topological relations the qualitative trajectory calculus on networks qtc n defines qualitative relations between two continuously moving point objects mpos moving along a network as prevailing in other research this network is presumed static in qtc n actually in many cases networks are dynamic entities for example in a road network the opening of a bridge can temporarily close the connection between two junctions traffic jams and traffic lights increase the time needed to travel from a to b therefore it is interesting to examine what happens with qualitative relations between two continuously moving point objects if there are changes in the network in this paper we introduce qtc d n being the qualitative trajectory calculus on changing networks able to handle topological network changes potential applications of the calculus in transportation are highlighted clearly illustrating the usefulness of the calculus

fuzzy scheduling modelling flexible constraints vs coping with incomplete knowledge abstract an overview of some fuzzy set based approaches to scheduling is proposed emphasizing two distinct uses of fuzzy sets representing preference profiles and modelling uncertainty distributions the first setting leads to a valued non compensatory generalization of constraint directed scheduling the other setting yields a possibility theoretic counterpart of pert where probability distributions of activity durations are changed into possibility distributions for the purpose of modelling incomplete information it is pointed out that a special case of the latter interval valued pert is a difficult ill known problem regarding the determination of critical activities latest starting times and floats lastly when flexible constraints and uncertain processing times are to be jointly considered the use of possibilistic decision theory leads to the computation of robust schedules

eigenmode analysis of arbitrarily shaped two dimensional cavities by the method of point matching in the proposed method as in the boundary element method bem a field problem is solved on its boundary along which nodes are distributed the distinct feature of the proposed method is related to the fact that no interpolation functions between the nodes are required so that the basic collocation method is employed to satisfy a given boundary condition this approach reduces a large amount of numerical calculation induced due to the interpolation functions unlike the method of auxiliary sources mas in the proposed method only the regular functions that have finite functional values everywhere including the origins are employed as basis functions as a result the proposed method does not need the auxiliary surface the construction of which is a troublesome work because its form dimension shifting etc strongly influence the accuracy of the mas the eigenvalues calculated by the proposed method rapidly converge to the exact values thanks to the simplicity of the method moreover the method gives mode shapes successfully without using the interpolation functions between the nodes the efficiency and accuracy of the method are verified through several applications

combining qualitative and quantitative constraints in temporal reasoning abstract this paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information this model allows the representation and processing of many types of constraints discussed in the literature to date including metric constraints restricting the distance between time points and qualitative disjunctive constraints specifying the relative position of temporal objects reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques such as backtracking and path consistency new classes of tractable problems are characterized involving qualitative networks augmented by quantitative domain constraints some of which can be solved in polynomial time using arc and path consistency

regularized meshless method for antiplane shear problems with multiple inclusions in this paper we employ the regularized meshless method to solve antiplane shear problems with multiple inclusions the solution is represented by a distribution of double layer potentials the singularities of kernels are regularized by using a subtracting and adding back technique therefore the troublesome singularity in the method of fundamental solutions mfs is avoided and the diagonal terms of influence matrices are determined an inclusion problem is decomposed into two parts one is the exterior problem for a matrix with holes subjected to remote shear the other is the interior problem for each inclusion the two boundary densities essential and natural data along the interface between the inclusion and matrix satisfy the continuity and equilibrium conditions a linear algebraic system is obtained by matching boundary conditions and interface conditions finally numerical results demonstrate the accuracy of the present solution good agreements are obtained and compare well with analytical solutions and gong s results

asymptotic stability of the fundamental solution method abstract in a previous paper 1988 we studied the numerical stability of the fundamental solution method applied to the dirichlet problem of laplace s equation and presented a practical scheme for examining the stability of the method using the singular value decomposition in the present paper we give an asymptotic estimate of the stability with respect to the number of collocation points

comment on eigenmode analysis of arbitrarily shaped two dimensional cavities by the method of point matching j acoust soc am 107 1153 2000 the method of point matching proposed by kang and lee j acoust soc am 107 1153 1160 2000 is revisited this method can be seen as a single layer potential approach from the viewpoint of imaginary part dual bem developed by chen et al j chin inst eng 12 729 739 1999 based on the concept of double layer potential an innovative method is proposed to deal with the problem of spurious eigensolution for the neumann problem also the acoustic mode is analytically derived for the circular cavity both the analytical study for a circular case and numerical result for a square cavity show the validity of the proposed formulation

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

supercuspidal characters of reductive p adic groups we compute the characters of many supercuspidal representations of reductive p adic groups specifically we deal with representations that arise via yu s construction from data satisfying a certain compactness condition each character is expressed in terms of a depth zero character of a smaller group the linear characters appearing in yu s construction fourier transforms of orbital integrals and certain signs and cardinalities that are described explicitly in terms of the datum associated to the representation and of the element at which the character is evaluated

solving partial differential equations by bkm combined with ddm the boundary knot method bkm has recently been developed as an inherently meshless integration free boundary type collocation technique for the numerical discretization of general partial differential equation systems unlike the method of fundamental solutions the use of non singular radial basis functions in the bkm avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain but the condition number of the coefficient matrix of the linear algebraic equations which is derived from the homogeneous boundary value problem becomes very high as the total number of boundary knots increase which in turn affects the accuracy of the computation result combined with domain decomposition method we can avoid this problem easily in this paper we will solve homogeneous and non homogeneous partial differential equations using bkm combined with overlapped ddm from the numerical experiments we can find that it can solve pdes accurately

boundary knot method based on geodesic distance for anisotropic problems the radial basis function rbf collocation techniques for the numerical solution of partial differential equation problems are increasingly popular in recent years thanks to their striking merits being inherently meshless integration free and highly accurate however the rbf based methods have markedly been limited to handle isotropic problems due to the use of the isotropic euclidean distance this paper makes the first attempt to use the geodesic distance with the rbf based boundary knot method bkm to solve 2d and 3d anisotropic helmholtz type and convection diffusion problems this approach is mathematically simple and easy to implement and spectral convergence is numerically observed for problems under complex shaped boundary numerical results show that the bkm based on the geodesic distance can produce highly accurate solutions of anisotropic problems with a relatively small number of knots this study provides a promising strategy for the rbf based methods to effectively solve anisotropic problems

fundamental solutions method for elliptic boundary value problems we consider a procedure for solving boundary value problems for elliptic homogeneous equations known as the fundamental solutions method we prove its applicability for some second order operators as well as for fourth order ones the boundary conditions of an elliptic problem are approximated by using fundamental solutions of the corresponding operator with singularities located outside the domain of interest in a specific case of the laplacian an estimate shows that the method discussed possesses convergence properties as good as those of any method using harmonic polynomials as trial functions numerical examples are given among which are simple signorini s problems for harmonic and lame operators

boundary knot method for 2d and 3d helmholtz and convection diffusion problems under complicated geometry the boundary knot method bkm of very recent origin is an inherently meshless integration free boundary type radial basis function collocation technique for the numerical discretization of general partial differential equation systems unlike the method of fundamental solutions the use of non singular general solution in the bkm avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain the purpose of this paper is to extend the bkm to solve 2d helmholtz and convection diffusion problems under rather complicated irregular geometry the method is also first applied to 3d problems numerical experiments validate that the bkm can produce highly accurate solutions using a relatively small number of knots for inhomogeneous cases some inner knots are found necessary to guarantee accuracy and stability the stability and convergence of the bkm are numerically illustrated and the completeness issue is also discussed

temporal reasoning based on semi intervals abstract a generalization of allen s interval based approach to temporal reasoning is presented the notion of conceptual neighborhood of qualitative relations between events is central to the presented approach relations between semi intervals rather than intervals are used as the basic units of knowledge semi intervals correspond to temporal beginnings or endings of events we demonstrate the advantages of reasoning on the basis of semi intervals 1 semi intervals are rather natural entities both from a cognitive and from a computational point of view 2 coarse knowledge can be processed directly computational effort is saved 3 incomplete knowledge about events can be fully exploited 4 incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps 5 there is no trade off in computational strength for the added flexibility and efficiency 6 for a natural subset of allen s algebra global consistency can be guaranteed in polynomial time 7 knowledge about relations between events can be represented much more compactly

least squares collocation meshless method a finite point method least squares collocation meshless method is proposed except for the collocation points which are used to construct the trial functions a number of auxiliary points are also adopted unlike the direct collocation method the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least squares sense the moving least squares interpolant is used to construct the trial functions the computational effort required for the present method is in the same order as that required for the direct collocation while the present method improves the accuracy of solution significantly the proposed method does not require any mesh so that it is a truly meshless method three numerical examples are studied in detail which show that the proposed method possesses high accuracy with low computational effort copyright 2001 john wiley sons ltd

temporal reasoning about fuzzy intervals traditional approaches to temporal reasoning assume that time periods and time spans of events can be accurately represented as intervals real world time periods and events on the other hand are often characterized by vague temporal boundaries requiring appropriate generalizations of existing formalisms this paper presents a framework for reasoning about qualitative and metric temporal relations between vague time periods in particular we show how several interesting problems like consistency and entailment checking can be reduced to reasoning tasks in existing temporal reasoning frameworks we furthermore demonstrate that all reasoning tasks of interest are np complete which reveals that adding vagueness to temporal reasoning does not increase its computational complexity to support efficient reasoning a large tractable subfragment is identified among others generalizing the well known ord horn subfragment of the interval algebra extended with metric constraints

the algebra ia fuz a framework for qualitative fuzzy temporal reasoning the aim of this work is to integrate the ideas of flexibility and uncertainty into allen s interval based temporal framework defining a new formalism called ia f u z which extends classical interval algebra ia in order to express qualitative fuzzy constraints between intervals we generalize the classical operations between ia relations to ia f u z relations as well as the concepts of minimality and local consistency referring to the framework of fuzzy constraint satisfaction problem we analyze the most interesting reasoning tasks in our framework which generalize the classical problems of checking consistency finding a solution and computing the minimal network in the context of ia in order to solve these tasks we devise two constraint propagation algorithms and a branch bound algorithm since these tasks are np difficult we address the problem of finding tractable sub algebras of ia f u z by extending to our fuzzy framework the classical pointizable sub algebras sa c and sa as well as the maximal tractable subalgebra h introduced by nebel in particular we prove that the fuzzy extension of the latter called h f u z shares with its classical counterpart a maximality property in that it is the unique maximal subalgebra of ia f u z which contains the fuzzy extensions of allen s atomic relations ions

semiring based constraint satisfaction and optimization we introduce a general framework for constraint satisfaction and optimization where classical csps fuzzy csps weighted csps partial constraint satisfaction and others can be easily cast the framework is based on a semiring structure where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain and the two semiring operations and x model constraint projection and combination respectively local consistency algorithms as usually used for classical csps can be exploited in this general framework as well provided that certain conditions on the semiring operations are satisfied we then show how this framework can be used to model both old and new constraint solving and optimization schemes thus allowing one to both formally justify many informally taken choices in existing schemes and to prove that local consistency techniques can be used also in newly defined schemes

reasoning about qualitative temporal information abstract representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks an interval based framework and a point based framework have been proposed for representing such temporal information in this paper we address two fundamental reasoning tasks that arise in applications of these frameworks given possibly indefinite and incomplete knowledge of the relationships between some intervals or points i find a scenario that is consistent with the information provided and ii find the feasible relations between all pairs of intervals or points for the point based framework and a restricted version of the interval based framework we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations our algorithms are marked improvements over the previously known algorithms in particular we develop an o n2 time algorithm for finding one consistent scenario that is an o n improvement over the previously known algorithm where n is the number of intervals or points and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm for the unrestricted version of the interval based framework finding a consistent scenario and finding the feasible relations have been shown to be np complete we show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems

a meshless integration free and boundary only rbf technique based on the radial basis function rbf nonsingular general solution and dual reciprocity method drm this paper presents an inherently meshless integration free boundary only rbf collocation technique for numerical solution of various partial differential equation systems the basic ideas behind this methodology are very mathematically simple in this study the rbfs are employed to approximate the inhomogeneous terms via the drm while nonsingular general solution leads to a boundary only rbf formulation for homogenous solution the present scheme is named as the boundary knot method bkm to differentiate it from the other numerical techniques in particular due to the use of nonsingular general solutions rather than singular fundamental solutions the bkm is different from the method of fundamental solution in that the former does not require the artificial boundary and results in the symmetric system equations under certain conditions the efficiency and utility of this new technique are validated through a number of typical numerical examples completeness concern of the bkm due to the sole use of the nonsingular part of complete fundamental solution is also discussed

the boundary collocation method with meshless concept for acoustic eigenanalysis of two dimensional cavities using radial basis function abstract in this paper a meshless method for the acoustic eigenfrequencies using radial basis function rbf is proposed the coefficients of influence matrices are easily determined by the two point functions in determining the diagonal elements of the influence matrices two techniques limiting approach and invariant method are employed based on the rbf in the imaginary part kernel the method results in spurious eigenvalues which can be separated by using the singular value decomposition svd technique in conjunction with the fredholm alternative theorem to understand why the spurious eigenvalues occur analytical study in the discrete system by discretizing the circular boundary is conducted by using circulants by using the svd updating terms and documents the true and spurious eigensolutions can be extracted out respectively several examples are demonstrated to see the validity of the present method

singular boundary method for solving plane strain elastostatic problems this study documents the first attempt to apply the singular boundary method sbm a novel boundary only collocation method to two dimensional 2d elasticity problems unlike the method of fundamental solutions mfs the source points coincide with the collocation points on the physical boundary by using an inverse interpolation technique to regularize the singularity of the fundamental solution of the equation governing the problems of interest three benchmark elasticity problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the mfs boundary element method bem and finite element method fem

novel meshless method for solving the potential problems with arbitrary domain in this article a non singular and boundary type meshless method in two dimensions is developed to solve the potential problems the solution is represented by a distribution of the kernel functions of double layer potentials by using the desingularization technique to regularize the singularity and hypersingularity of the kernel functions the source points can be located on the real boundary and therefore the diagonal terms of influence matrices are determined the main difficulty of the coincidence of the source and collocation points then disappears by employing the two point function the off diagonal coefficients of influence matrices are easily obtained the numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of exact solution conventional mfs and bem for the dirichlet neumann and mix type boundary conditions bcs of interior and exterior problems with simple and complicated boundaries good agreements with exact solutions are observed

a localized approach for the method of approximate particular solutions the method of approximate particular solutions maps has been recently developed to solve various types of partial differential equations in the maps radial basis functions play an important role in approximating the forcing term coupled with the concept of particular solutions and radial basis functions a simple and effective numerical method for solving a large class of partial differential equations can be achieved one of the difficulties of globally applying maps is that this method results in a large dense matrix which in turn severely restricts the number of interpolation points thereby affecting our ability to solve large scale science and engineering problems in this paper we develop a localized scheme for the method of approximate particular solutions lmaps the new localized approach allows the use of a small neighborhood of points to find the approximate solution of the given partial differential equation in this paper this local numerical scheme is used for solving large scale problems up to one million interpolation points three numerical examples in two dimensions are used to validate the proposed numerical scheme

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations

free vibration analysis of arbitrarily shaped plates with clamped edges using wave type functions the basic idea related to the non dimensional dynamic influence green s function defined in an infinite membrane has been applied to the free vibration analysis of arbitrarily shaped plates with clamped edges another non dimensional dynamic influence function newly defined in the paper exactly satisfies the governing homogeneous differential equations of plates and is regular in the entire domain the proposed method uses the boundary discretization scheme similar to that of the boundary element method but does not require any interpolation function between the nodes distributed along the boundary as a result the method has a significant advantage in its simplicity and accuracy although the method uses no interpolation function it gives very accurate eigenvalues and mode shapes compared with the exact solutions or fem results it should be also noted that particular attention is given to reduce the size of the system matrix whose determinant equation yields eigenvalues and to overcome the functional dependence problem of the non dimensional dynamic influence functions

numerical investigation on convergence of boundary knot method in the analysis of homogeneous helmholtz modified helmholtz and convection diffusion problems abstract this paper concerns a numerical study of convergence properties of the boundary knot method bkm applied to the solution of 2d and 3d homogeneous helmholtz modified helmholtz and convection diffusion problems the bkm is a new boundary type meshfree radial function basis collocation technique the method differentiates from the method of fundamental solutions mfs in that it does not need the controversial artificial boundary outside physical domain due to the use of non singular general solutions instead of the singular fundamental solutions the bkm is also generally applicable to a variety of inhomogeneous problems in conjunction with the dual reciprocity method drm therefore when applied to inhomogeneous problems the error of the drm confounds the bkm accuracy in approximation of homogeneous solution while the latter essentially distinguishes the bkm mfs and boundary element method in order to avoid the interference of the drm this study focuses on the investigation of the convergence property of the bkm for homogeneous problems the given numerical experiments reveal rapid convergence high accuracy and efficiency mathematical simplicity of the bkm