a back propagation artificial neural network (bpann) is a well-known learning algorithmpredicated on a gradient descent method that minimizes the square error involving the networkoutput and the goal of output values. in this study, 261 gps/leveling and 8869 gravity intensityvalues of iran were selected, then the geoid with three methods “ellipsoidal stokes integral”,“bpann”, and “collocation” ...

We propose and analyze a numerical method for solving fourth order differential equations modelling two point boundary value problems. The scheme is based on B-splines collocation. The error analysis is carried out and convergence rates are derived.

This paper focuses on automatic determination of the distributional preferences of words in Russian. We present the comparison of six different measures for collocation extraction, part of which are widely known, while others are less prominent or new. For these metrics we evaluate the semantic stability of automatically obtained bigrams beginning with singletoken prepositions. Manual annotatio...

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

A class of numerical methods is developed for second order Volterra integrodifferential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the L∞-norm and L-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods. AMS subject classifica...

A nonlinear Dirichlet boundary value problem is approximated by an orthogonal spline collocation scheme using piecewise Hermite bicubic functions. Existence, local uniqueness, and error analysis of the collocation solution and convergence of Newton’s method are studied. The mesh independence principle for the collocation problem is proved and used to develop an efficient multilevel solution met...

the aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. the state and co-state are approximated by the lowest order raviart-thomas mixed finite element spaces and the control is not discreted. optimal error estimates in l2 are established for the state...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

In this paper, some enhanced error estimates are derived for the augmented subspace methods which designed solving eigenvalue problems. For first time, we strictly prove that have second order convergence rate between two iteration steps, is better than existing theoretical results in Lin and Xie (Math Comp 84:71–88, 2015), et al. (SIAM J Numer Anal 57(6):2519–2550, 2019), Xu Sci Comput 42(5):A...