We present a constructive proof of Brouwer’s fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions based on the existence of approximate fixed points. And we will show that our Brouwer’s fixed point theorem implies Sperner’s lemma for a simplex. Since the existence of approximate fixed points is derived from Sperner’s lemma, our Brouwer’s fixe...

‎in this paper‎, ‎an approach based on statistical spline model (ssm) and collocation method is proposed to solve volterra-fredholm integral equations‎. ‎the set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎numerical results on some problems are given...

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

We consider the methods of construction simple polygons for a set S of n points and applying them for searching the minimal area polygon. In this paper we propose the approximate algorithm, which generates the simple polygonalizations of a fixed set of points and finds the minimal area polygon, in O (n) time and using O(n) memory. Keywords—simple polygon, approximate algorithm, minimal area pol...

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

in this research three-dimensional free vibration analysis of functionally graded circular plate with various boundary conditions is achieved. a semi-analytical method, which makes use of the state space method and the one-dimensional differential quadrature method, is used to obtain the vibration frequencies and dynamic responses of circular plates. numerical results are given to demonstrate t...

Geospatial joins are a core building block of connected mobility applications. An especially challenging problem are joins between streaming points and static polygons. Since points are not known beforehand, they cannot be indexed. Nevertheless, points need to be mapped to polygons with low latencies to enable real-time feedback. We present an approximate geospatial join that guarantees a user-...

Standard software based on the collocation method for differential equations, delivers a continuous approximation (called the collocation solution) which augments the high order discrete approximate solution that is provided at mesh points. This continuous approximation is less accurate than the discrete approximation. For ’non-standard’ Volterra integro-differential equations with constant del...