In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. This nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. By using operational matrix of fractional integration...

sinc-galerkin method based upon double exponential transformation for solving troesch's problem was given in this study. properties of the sinc-galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.the error bound of the method was fo...

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 are used 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 ana...

this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

Sinc-Galerkin method based upon double exponential transformation for solving Troesch's problem was given in this study. Properties of the Sinc-Galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.The error bound of the method was found. ...

in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.