In this paper, the differential transformation (DTM) and Adomian decomposition (ADM) methods are proposed for solving fourth order eigenvalue problem. This problem has nonstrongly regular boundary conditions. been examined p(t) = t, B 0, a 0,01 where ≠ 0 is complex valued The briefly described. An approximate solution obtained by performing seven iterations with method. same number of have made...

In this paper, a newsboy model is developed under uniformly distributed lead-time and demand that is an appropriate assumption in obtaining optimal relief inventory of humanitarian disasters. It is noteworthy that limited historical data are in hand on relief operations. Hence, analytical and approximate solutions for optimal relief order quan­tity were derived. The effect of lead-time uncertai...

In this paper, vibrations and bifurcation of a damped system consists of a mass grounded by linear and nonlinear springs and a nonlinear damper is studied. Nonlinear equation of motion is derived using Newton’s equations. Approximate analytical solutions are obtained using multiple time scales (MTS) method. For free vibration, the approximate analytical results are compared with the numerical i...

This paper demonstrates a study on some significant latest innovations in the approximated techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To this aim, the study uses the modified Adomian decomposition method (MADM) and the modified variational iteration method (MVIM). A wider applicability of these techniques are based on thei...

The nonlinear dynamical system modeling the immobilized enzyme kinetics with Michaelis-Menten mechanism for an irreversible reaction without external mass transfer resistance is considered. Laplace transform homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

in this paper, the bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (iemtl) through expansion methods (collocation method, partition method, galerkin method). the method is discussed in detail and illustrated by solving some numerical examples. comparison between the exact and approximated results obtained from these methods is...

The basic solutions of the linear equation Ax = b , are the solutions of subsystems corresponding to maximal nonsingular submatrices of A. The convex hull of the basic solutions is denoted by C = C(A,b). The residual r(x) of a vector x is r := Ax − b. Given 1 ≤ p ≤ ∞, the lp-approximate solutions of Ax = b, denoted x , are minimizers of ‖r(x)‖p. Given M ∈ Dm, the set of positive diagonal m×m ma...

Evolutionary algorithms have been recognized to be suitable for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier‎. ‎This paper applies an evolutionary optimization scheme‎, ‎inspired by Multi-objective Invasive Weed Optimization (MOIWO) and Non-dominated Sorting (NS) strategi...

The knowledge of exact symmetries of a diierential problem allows to reduce it, and sometimes to completely solve it; it also allows to obtain exact solutions. If we are looking for approximate rather than exact solutions, then approximate symmetries are as good as exact ones; moreover, they can be determined perturbatively. In this paper we introduce and study approximate symmetries, together ...