this paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (msham). the proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. several illustrat...

New Runge–Kutta methods for method of lines solution of systems of ordinary differential equations arising from discretizations of spatial derivatives in hyperbolic equations, by Chebyshev or modified Chebyshev methods, are introduced. These Runge–Kutta methods optimize the time step necessary for stable solutions, while holding dispersion and dissipation fixed. It is found that maximizing disp...

in this paper, the chebyshev spectral collocation method(cscm) for one-dimensional linear hyperbolic telegraph equation is presented. chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. a straightforward implementation of these methods involves the use of spectral differentiation matrices. firstly, we transform ...

Abstract. In this paper, a numerical solution for the system described by a generalized fractional Rikitake system is presented. The first step in the proposed procedure is represent the fractional order Rikitake system as an equivalent system of ordinary differential equations. In the second step, we solved the system obtained in the first step by using the well known fourth order Runge-Kutta ...

In this paper, a fractional order HIV/AIDS (FOHA) epidemic model with treatment is investigated. The first step in the proposed procedure is represent the FOHA system as an equivalent system of ordinary differential equations. In the second step, we solved the system obtained in the first step by using the well known fourth order Runge-Kutta method. Numerical simulations are also presented to v...

 In this paper, we investigate the evolution of supercontinuum and femtosecond optical pulses generation through square lattice elliptical-core photonic crystal fiber (PCF) at 1550 nm by using both full-vector multipole method (M.P.M) and novel concrete algorithms: symmetric  split-step Fourier (SSF) and  fourth order Runge Kutta (RK4) which is an accurate method to solve the general  nonlinear...

Three new Runge–Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODEs) with constant coefficients. Such ODEs arise in the numerical solution of partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of...

Abstract This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme spatial part combined implicit-explicit Runge Kutta in temporal are proposed. Furthermore, points discretized by using terms fourth order accuracy. key idea proposed is take full advan...

Abstract. Purely dispersive equations, such as the Korteweg-de Vries and the nonlinear Schrödinger equations in the limit of small dispersion, have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral ...