This research considers a symmetric hybrid continuous linear multistep method for the solution of general third order ordinary differential equations. The method is generated by interpolation and collocation approach using a combination of power series and exponential function as basis function. The approximate basis function is interpolated at both grid and off-grid points but the collocation ...

Understanding the error structures of remotely sensed soil moisture observations is essential for correctly interpreting observed variations and trends in the data or assimilating them in hydrological or numerical weather prediction models. Nevertheless, a spatially coherent assessment of the quality of the various globally available datasets is often hampered by the limited availability over s...

In this paper, two collocation methods based on the shifted Legendre polynomials are proposed for solving system of nonlinear Fredholm-Volterra integro-differential equations. The equation considered in paper involves derivative unknown functions integral term, which makes its numerical solution more complicated. We first introduce a single-step method interval [0, 1]. Next, multi-step version ...

The detection of abbreviations is an important step in the process of sentence boundary detection. We describe a flexible, languageindependent and accurate method based on the idea that an abbreviation can be viewed as a collocation. As such, it can be identified by using methods for collocation detection such as the log likelihood ratio. Although the log likelihood ratio is known to show a goo...

Abstract The main aim of the current paper is to construct a numerical algorithm for solutions second-order linear and nonlinear differential equations subject Robin boundary conditions. A basis function in terms shifted Chebyshev polynomials first kind that satisfy homogeneous conditions constructed. It has established operational matrices derivatives constructed polynomials. obtained are spec...

Richardson extrapolation is applied to improve the accuracy of the numerical solution of boundary integral equations. The boundary integral equations arise from a direct boundary integral method for solving a Laplace’s equation interior Dirichlet problem. Specifically, the Richardson extrapolation is used to improve the accuracy of collocation. Numerical justification is provided to support the...

In this talk, we are concerned with embedded formulae of the Chebyshev collocation methods [1] developed recently. We introduce two Chebyshev collocation methods based on generalized Chebyshev interpolation polynomials [2], which are used to make an automatic integration method. We apply an elegant algorithm of generalized Chebyshev interpolation increasing the node points to make an error esti...

This paper introduces an effective H-adaptive upgrade to solution of the transport phenomena by the novel Local Radial Basis Function Collocation Method (LRBFCM). The transport variable is represented on overlapping 5-noded influence-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the variable are calculated from the ...