In this paper, the existence and uniqueness theorems for a solution to an uncertain characteristic Cauchy reaction-diffusion problem is studied by Adomian decomposition method. Sufficient conditions are presented for uniform convergence of the proposed method. Also, some illustrative examples are given for solving the problem. Key WordsUncertain characteristic Cauchy problem, System of characte...

where f(t),g(t), and h(t) are known continuous functions of t in the interval (0,1). Here N(u) is a nonlinear function of u. Let the above equation be singular at these two boundary value points t= 0,1. Scientists and engineers are interested in singular BVPs because they arise in a wide range of applications, such as in chemical engineering, mechanical engineering, nuclear industry, and nonlin...

The vibration problems of uniform and nonuniform Euler-Bernoulli beams have been solved analytically or approximately [1-5] for various end conditions. In order to calculate fundamental natural frequencies and related mode shapes, well known variational techniques such as Rayleigh_Ritz and Galerkin methods have been applied in the past. Besides these techniques, some discretized numerical metho...

The topic of the Adomian decomposition method has been rapidly growing in recent years. The concept of this method was first introduced by G. Adomian in the beginning of 1980’s [1, 2]. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution [3]. The Adomian decomposition method for solving linear and nonlinear integ...

Adomian decomposition method, as a convenience device has been used to solve many functional equations so far. In this manuscript, we consider a system of nonlinear ordinary differential equations, which governs on general reaction in biochemistry as a theoretical problem of concentration kinetics. These system, which is known as Brusselator system has been solved by applying Adomian decomposit...

we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.

Since 2001, Laplace decomposition algorithm (LDA) has been one of the reliable mathematical methods for obtaining exact or numerical approximation solutions for a wide range of nonlinear problems. The Laplace decomposition algorithm was developed by Khuri in [2] to solve a class of nonlinear differential equations. The basic idea in Laplace decomposition algorithm, which is a combined form of t...

Although the decomposition method and its modified form were used during the last two decades by many authors to investigate various scientific models, a little attention was devoted for their applications in the field of fluid mechanics. In this paper, the Adomian decomposition method (ADM) is implemented for solving the nonlinear partial differential equation (PDE) describing the peristaltic ...

In this paper, it is revealed that Adomian decomposition method corresponds to Taylor series method when applied to the solution of nonlinear initial value problems, in the following sense: the Adomian ́s polynomials can be obtain trough Taylor coefficients.

Decomposition method was first introduced by Adomian since the beginning of the 1980’s for solving wide range of problems whose mathematical models yield equation or system of equation involving algebraic, differential, integral and integro-diffrential [1, 2, 3]. This iterative method has been proven to be rather successful in dealing with linear problems as well as nonlinear. Adomian gives the...