Adomian decomposition method for nonlinear reaction diffusion system of Lotka-Volterra type

Abstract

In this paper the Adomian decomposition method is used to find an analytic approximate solution for nonlinear reaction diffusion system of Lotka-Volterra type. The results obtained indicate that the method is efficient and accurate.

Homotopy Method for Solving Finite Level Fuzzy Nonlinear Integral Equation

“…The following properties are satisfied for all α ∈ E0 1-The set of all level α ∈ E0,1F, that represent distinct α -cuts of a given fuzzy set [17] A " is called a level set of A " Λ A " = $α|μ ) " (x) = α, for some x ∈ X} 2-The support of A " is exactly the same as the strong α − cut of A " for α = 0 , A TU = S A " .…”

“…Definition 14: Starting from the fuzzy mapping F : X → P " (x) with μ Ö " (0) : X → I, for any α ∈ (0,1], we can define the α − cut of F , denoted by F J as follows [17,24]:…”

“…The fuzzy function f (x) is supposed to be fuzzy number; we shall further assume that α -level curves [3,8,17]: 1-A fuzzy mapping having a one curve will be called a normalized fuzzy mapping 2-A continuous fuzzy mapping is a fuzzy mapping f (x) such that μ b (0) (y) is continuous for all x ∈ I ⊂ R, and all y ∈ R 3-The concept of fuzzy interval is convex, normalized fuzzy set of R whose membership function is continuous. Definition 16:.A fuzzy mapping F such that F : X → p (X) , in other words, to each x ∈ X, corresponds a fuzzy F (x) deëined on X, whose membership function is μ Ö ": X → I.…”

On using the modified variational iteration method for solving the nonlinear coupled equations in the mathematical physics

“…Various powerful methods for obtaining the exact solutions for the nonlinear partial differential equations have been proposed (see, for example ). Among of these methods are Bäcklund transformation method [12,[31][32][33], the inverse scattering transform method , extended tanh method [9][10][11][12][13], Adomian Pade approximation [28], variational iteration method [5,6,9,17,22,30], homotopy perturbation method [18][19][20]23,40,41], various Lindstedt-Poincare methods [21,22], Adomian decomposition method [1][2][3][4]8,10,11,16,24,26,27,40], F-expansion method [34], exp-function method [35], the Jacobi elliptic function expansion method [37], the complex hyperbolic function method [39] and so on. The objective of this paper is to use the modified variational iteration method (MVIM) to solve the generalized nonlinear Hirota Satsuma coupled KdV equations [14,15,37,38] …”

The Convergence Analysis of the Decomposition Method for the (1+1)-Parabolic Problem in Nonuniform Media

“…The method can be mechanized in Maple and a procedure is written to solve the approximate analytic solution of the systems. Analytic approximated solution for nonlinear reaction diffusion system of Lotka-Volterra type were obtained by Alabdullatif, Abdusalam and Fahmy [6]. Afrouzi and Khademloo applied the ADM to a quasilinear parabolic equation.…”