Adomian decomposition method is extended to the calculations of the non-differentiable functions. The iteration procedure is based on Jumarie’s Taylor series. A specific fractional differential equation is used to elucidate the solution procedure and the results are compared with the exact solution of the corresponding ordinary differential equations, revealing high accuracy and efficiency. © 2...

In this paper the Adomian decomposition method is applied to the nonlinear SturmLiouville problem −y + y(t) = λy(t), y(t) > 0, t ∈ I = (0, 1), y(0) = y(1) = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.

In this work, the solution of a boundary value problem is discussed via a semi analytical method. The purpose of the present paper is to inspect the application of the Adomian decomposition method for solving the Nagumo telegraph equation. The numerical solution is obtained for some special cases so that demonstrate the validity of method.

In the present paper we obtain closed form solutions of spacetime fractional telegraph equations using Adomian decomposition method. The space and time fractional derivatives are considered as Caputo fractional derivative and the solutions are obtained in terms of Mittag-Leffler functions.

Solution of homogeneous fuzzy partial differential equations with specific fuzzy boundary and initial conditions are proposed. Using Adomian Decomposition method, we solve the heat equations for which it is difficult to find the solution by classical methods. We extend the crisp solution in the fuzzy form as a Seikkala solution. MSC: 34A07 • 35K51

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...

Let a singular value of a bidiagonal matrix be known. Then the corresponding singular vector can be computed through the twisted factorization of a tridiagonal matrix by the discrete Lotka-Volterra with variable step-size (dLVv) transformation. Errors of the singular value then sensitively affect the conditional number of the tridiagonal matrix. In this paper, we first examine a relationship be...

In order to solve the local fractional differential equations, we couple residual method with Adomian decomposition via calculus operator. Several examples are given illustrate solution process and reliability of method.

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...