in this paper, differential transform method (dtm) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in hiv infections of cell. intervals of validity of the solution will be extended by using pade approximation. the results also will be compared with those results obtained by runge-kutta method. the technique is described and is illustrat...

In this work we consider Symplectic Runge Kutta Nyström methods with five stages. A new fourth algebraic order method with phase-lag order eight is presented. Also the symplectic Runge Kutta Nyström of Calvo and Sanz Serna with five stages and fourth order is modified to produce a phase-fitted method. We apply the new methods on several Hamiltonian systems and on the computation of the eigenval...

In this paper, we analyze the stability of the fourth order Runge-Kutta method for integrating semi-discrete approximations of time-dependent partial differential equations. Our study focuses on linear problems and covers general semi-bounded spatial discretizations. A counter example is given to show that the classical four-stage fourth order Runge-Kutta method can not preserve the one-step st...

In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally ...

In this paper, based on the classical Fourth-Order Runge-Kutta method, the modified FourthOrder Runge-Kutta method is presented for solving nonlinear vibration of axially travelling string system, that is to solve time varying and nonlinear differential equations. The classical Fourth-Order Runge-Kutta method can only be used to solve first-order linear differential equations. Its main idea is ...

This paper presents an overview of high-order implicit time integration methods and their associated properties with a specific focus on their application to computational fluid dynamics. A framework is constructed for the development and optimization of general implicit time integration methods, specifically including linear multistep, Runge-Kutta, and multistep Runge-Kutta methods. The analys...

This study utilised positive Lyapunov exponents’ criteria to develop chaos diagram on the parameters space of 4-dimensional harmonically excited vibration absorber control Duffing’s Oscillator. Relevant simulations were effected by choice combination of constant step Runge-Kutta methods and Grahm Schmidt Orthogonal rules. Simulations of 4-dimensional hyper-chaotic models of modified Lorenz and ...

In this paper, a hybrid technique of differential quadrature method and Runge-Kutta fourth order method is employed to analyze reaction-diffusion problems. The obtained results are compared with the available analytical ones. Further, a parametric study is introduced to investigate the influence of reaction and diffusion characteristics on behavior of the obtained results. Index Term-Reaction-d...

Sugiura, H. and T. Torii, A method for constructing generalized Runge-Kutta methods, Journal of Computational and Applied Mathematics 38 (1991) 399-410. In the implementation of an implicit Runge-Kutta formula, we need to solve systems of nonlinear equations. In this paper, we analyze the Newton iteration process and a modified Newton iteration process for solving these equations. Then we propo...