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...

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...

The ultimate goal of this study is to develop a numerically effective approximation technique acquire numerical solutions the integer and fractional-order Bratu singular Lane–Emden-type problems especially with exponential nonlinearity. Both initial boundary conditions were considered fractional derivative being in Liouville–Caputo sense. In direct approach, generalized Bessel matrix method bas...

An adaptive block elimination method based on recursive projection techniques is proposed for solving large linear systems which arise when applying Newton methods to parameter dependent nonlinear equations. The method is suitable for non-linear systems that have a Jacobian with a symmetric and almost positive deenite main block. The implicitly deened large symmetric and positive deenite subsys...

As one of themost important subjects of mathematics, differential and integral equations are widely used to model a variety of physical problems. Perturbation methods have been used in search of approximate analytical solutions for over a century [1–3]. Algebraic equations, integral-differential equations, and difference equations could be solved by these techniques approximately. However, a ma...

Bratu‐type equation has wide applications in physics, finance, and other fields. Also, fractional analysis been a popular topic recently. It is difficult to find the analytical solution once we add operator on left side of equation. In this work, apply explicit implicit finite difference methods solve Bratu From numerical examples, will see that not accurate, based Newton's method efficient som...

The aim of this study is applying the Multistage Adomian Decomposition Method (MADM), based on the Adomian Decomposition Method (ADM) to solve an initial value problem of Bratu-type. The approximat-ed solutions are computed and then the numerical results compared those of ADM, Finally comparisons of the results show that the pro-posed method is very effective and accurate.