The immense explosion of geographically referenced data calls for efficient discovery of spatial knowledge. Spatial association analysis is a typical data mining approach for discovering spatial knowledge. Associate rules are patterns of form X→Y, where pattern Y is likely to occur when pattern X occurs. One of the most famous patterns, Diapers → Beer, is a typical association rule example. Spa...

Though the technique introduced by E. Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail–safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test...

Several numerical methods for approximating the solution of Hammerstein integral equations are known. For Fredholm-Hammerstein integral equations, the classical method of successive approximations was introduced in [16]. A variation of the Nystrom method was presented in [11]. A collocation-type method was developed in [9]. In [3], Brunner applied a collocation-type method to nonlinear Volterra...

We present a meshless technique which can be seen as an alternative to the Method of Fundamental Solutions (MFS). It calculates homogeneous solutions of the Laplacian (i.e. harmonic functions) for given boundary data by a direct collocation technique on the boundary using kernels which are harmonic in two variables. In contrast to the MFS, there is no artifical boundary needed, and there is a f...

This paper illustrates the use of the differentiation matrix technique for solving differential equations in finance. The technique provides a compact and unified formulation for a variety of discretisation and time-stepping algorithms for solving problems in one and two dimensions. Using differentiation matrix models, we compare time-stepping algorithms for option pricing computations and pres...

The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linea...

The paper aims at serving two goals. Firstly, attention will be drawn to a class of collocations that, to our knowledge at least, has gone unnoticed so far. Secondly, it will be argued that brute force techniques as they are employed by certain automated collocation search strategies using a quantitative technique plus a mechanism to filter out unwanted combinations is a guaranteed way to miss ...

The importance and howness of language learning/ acquisition has been a great concern for decades. There are many factors that play important roles in this regard. This research compared the performance of native Persian and English elementary students to see if there is any significant difference between the two groups and which type of collocation they performed better within the groups. For ...

In this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocatio...

In this chapter, the indirect Trefftz collocation method is applied to solve the inverse Cauchy problem of linear piezoelectricity. The static analysis of coupled fields in 2D piezoelectric solids is considered. The piezoelectric material is modelled as a homogenous, linear elastic, linear dielectric and transversal isotropic. The T-functions are obtained by the Stroh formalism. The inverse Cau...