We introduce a new method, namely, the Optimal Iteration Perturbation Method OIPM , to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solution...

Perturbation–iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation–iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation–iteration algorithms, new solutions of Bratu-type equations ...

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations unsteady flow a polytropic gas. The methods suggested are modified forms variational iteration method and homotopy perturbation by Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify accuracy available techniques. A graphical representation...

An analytic iteration sequence based on the extension of BLUES (Beyond Linear Use Equation Superposition) function method to partial differential equations (PDEs) with second-order time derivatives is studied. The original formulation modified by introducing a matrix formalism that takes into account initial conditions for higher-order derivatives. both solution and its now play role source vec...

objectives: to check and compare the effectiveness of modified agility and perturbation training over conventional physical therapy in patients with knee osteoarthritis. methods: subjects were screened on the basis of inclusion and exclusion criteria and a total of 50 subjects were recruited for the study. they were randomly divided into group a and group b with n=25 each. results: group receiv...

Newton’s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton’s iteration can be done efficiently. We show that the convergence of the modifie...

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the meth...