Global error bounds are derived for Runge-Kutta time discretizations of fully nonlinear evolution equations governed by m-dissipative vector fields on Hilbert spaces. In contrast to earlier studies, the analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants in order to extend the classical B-convergence theory to...

In this investigation, an (un)forced third-order/jerk Van-der Pol oscillatory equation is solved using two perturbative methods called the Krylov–Bogoliúbov–Mitropólsky method and multiple scales method. Both first- second-order approximations for unforced forced jerk equations are derived in detail proposed methods. Comparative analysis performed between analytical numerical fourth-order Runge...

Implicit Runge-Kutta methods are considered which combine the single-implicitness or diagonal-implicitness property with a zero first row in the coefficient matrix. Acceptable stability for stiff problems is retained by requiring the last stage of a step to be identical to the output value. This requirement, which corresponds to the FSAL property for explicit Runge-Kutta methods, allows the met...

Galerkin fully discrete approximations for parabolic equations with time-dependent coefficients are analyzed. The schemes are based on implicit Runge-Kutta methods, and are coupled with preconditioned iterative methods to approximately solve the resulting systems of linear equations. It is shown that for certain classes of Runge-Kutta methods, the fully discrete equations exhibit parallel featu...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

in this article, we present a fractional order hiv-1 infectionmodel of cd4+ t-cell. we analyze the effect of the changing the averagenumber of the viral particle n with initial conditions of the presentedmodel. the laplace adomian decomposition method is applying to checkthe analytical solution of the problem. we obtain the solutions of thefractional order hiv-1 model in the form of infinite se...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

In this study we develop high order numerical methods to capture the spatiotemporal dynamics of a generalized Kolmogorov-Petrovskii-Piskunov (KPP) equation characterized by density dependent non-linear diffusion. Towards this direction we consider third order Strong Stability Preserving Runge-Kutta (SSPRK) temporal discretization schemes coupled with the fourth order Hermite cubic Collocation (...

The orbital dynamics of an artificial satellite in the Earth’s atmosphere is considered. An analytic first-order atmospheric drag theory is developed using Lagrange’s planetary equations. The short periodic perturbations due to the geopotential of all orbital elements are evaluated. And to construct a second-order analytical theory, the equations of motion become very complicated to be integrat...