Abstract: In this paper Differential Transform Method (DTM) is implemented to solve some Riccati differential equations with variable co-efficients. This technique doesn’t require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. The results derived by this method are compared with the numerical results by Runge Kutta 4 (R...

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

We present two numerical methods for the approximation of the generalized Zakharov system (ZS). The first one is the time-splitting spectral (TSSP) method, which is explicit, time reversible, and time transverse invariant if the generalized ZS is, keeps the same decay rate of the wave energy as that in the generalized ZS, gives exact results for the plane-wave solution, and is of spectral-order...

in this paper, the approximate solution of the differential system modeling hiv infection of cd4+ t cells isobtained by a reliable algorithm based on an adaptation of the standard variational iteration method (vim), which is called the multi-stage variational iteration method(msvim). a comparison between msvim and the fourthorder runge-kutta method (rk4-method) reveal that the proposed techniqu...

This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense. The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton iteration meth...

This study is divided into two important axes; for the first one, a new symmetric analytical (approximate) solution to Duffing–Helmholtz oscillatory equation in terms of elementary functions derived. The obtained compared with numerical using 4th Range–Kutta (RK4) approach and exact that elliptic functions. As second axis, we consider time-delayed version same oscillator taking impact both forc...

In this paper, an effective algorithm which is a combination of the spectral collocation method and the parametric iteration method (PIM) is proposed for simulating the solution of the chaotic Genesio system (CGS). Comparison with the fourth-order Runge–Kutta method (RK4) confirms the very high accuracy of the presented algorithm. The obtained results reveal that the proposed algorithm is a pro...

A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of oscillation model between Euler method symplectic method, four-order Runge–Kutta (RK4) Runge–Kutta–Nyström (SRKN4), RK4 SRKN4 in preserving structure are compared from theoretical numerical simulations, symmetry stability scheme demonst...

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the...