Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

In this study, the main features of the Boubaker Polynomials Expansion Scheme (BPES) are outlined on the basis of published, compared and confirmed solution to differently established appliedphysics nonlinear problems. Some new applications of the same scheme in the field of fluids motion and waves dynamics are also discussed. PACS: 2010 02.30.Jr; 02.30.Sa

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

In this paper, the He’s parameter-expanding method (HPEM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES) are used in order to obtain analytical solutions to the non-linear modified Van der Pol’s oscillating circuit equation. The resolution protocols are applied to the ordinary Van der Pol equation, which annexed to conjoint delayed feedback and delay-related damping terms. The results ...

Abstract The object of this paper is to develop an accurate combined spectral collocation approach numerically solve the generalized nonlinear Benjamin–Bona–Mahony–Burgers equation. first stage devoted discretization in time, which carried out with aid well-known Taylor series expansions. Then procedure based on Boubaker polynomials applied for resulting discretized spatial operator each time s...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...