... Differential equations Polynomials Nonlocal boundary value problems Sturm‐Liouville boundary value problems Nonlinear differential equations Adomian decomposition method Adomian polynomials Many physical phenomena, both in classical and quantum mechanics, are described mathematically by Sturm...

... equations. © Emerald Group Publishing Limited 2012 Mathematics Integral equations Polynomials Volterra integral equation System of first and second kind Algebraic system Discretization Collocation method Chebyshev polynomials System of Volterra integral equations is defined...

..., … ,x ′_{n) when α tends to zero. Esther Claudine Bitye Mvondo can be contacted at: esther.bitye@neuf.fr © Emerald Group Publishing Limited 2012 Polynomials Algebra Operational research Global optimization Integer programming Number theory Diophantine}...

.... J.M. Sepulcre can be contacted at: jm.sepulcre@ua.es © Emerald Group Publishing Limited 2012 Polynomials Zeros of entire functions Exponential polynomials Partial sums of the Riemann zeta function By the partial sums of the Riemann zeta function we will mean the entire functions...

... algorithms are proposed in recent years dealing with getting the numerical solution of advection‐diffusion equation. İdris Dağ can be contacted at: idag@ogu.edu.tr © Company 2011 Cybernetics Diffusion Polynomials Applications of methods based on spline functions have studied from...

... Cybernetics Differential equations Systems theory Mathematics Polynomials In our previous paper (Ben Zitoun and Cherruault, 2009a, b), we have introduced a technique for solving nonlinear boundary value problems. In the present work, our aim is to present a modified form of this technique...

... Equation 11 Let us approximate u(x) in V₁ by the polynomial of degree N: Equation 12 then: Equation 13 where u_approx^(s)(x) denotes the sth derivative of u_approx(x). Hence: Equation 14...

..., A_n{(g∘u)}(u₀,u₁, … ,u_{n)∈R. Let us approximate u(x) in V1 by the truncated Taylor series: Equation 6 which is a Taylor polynomial of degree N at x=c. Feyed Ben Zitoun can}...

... polynomial. Design/methodology/approach Since there are limitations in two‐dimensional sequential uniform design, three‐dimensional sequential uniform design introduced in this paper is to arrange the experimental points by U₉(9³) uniform design table and to determine...

... for searching solutions to the multi‐dimensional transport problems, leads us to a solution for all values of the independent variables. Research limitations/implications The procedure is based on the development of the angular flux in a truncated series of Chebyshev polynomials in the spatial variables...

... Equation 32   Table II shows that using the Taylor polynomials method in Yalçinbas and Sezer (2000) , ten iterations were evaluated to obtain the same results provided by the decomposition method where only four components were computed which is equal to the exact solution. Furthermore, the decomposition...

... ; Adomain, 1994; Cherruault, 1998, 1999). Cybernetics Polynomials Boundary‐elements methods In recent years, singular two‐point boundary value problems in the second‐order ordinary differential equation have been studied by many mathematicians and physicists. In the present work, we...

... A_ns are Adomian's polynomials of y₀,y₁, … ,y_n given by Adomian (1986, 1994) . A new algorithm was established for Adomian polynomials by Wazwaz (2000b). Upon substituting equations (7) and (8) into equation (6) yields Equation...

... the Mathematica software package can be used in such studies. © Emerald Group Publishing Limited 2005 Cybernetics Polynomials Non‐linear control systems The recent years have seen a significant development in the use of various methods for the numerical and analytic solution of partial...

... A_n and A˜_n are the Adomian polynomials. Hence, upon substituting these decomposition series into yields Equation 12 From the iterates are then determined in the following recursive way: Equation 13 Equation 14 For the case where the non‐linear terms N₁=−u³...