Many physical problems in the real world are frequently modeled by ordinary differential equations (ODEs). Real-life usually non-linear, numerical methods therefore needed to approximate their solution. We consider different viz., Explicit (Forward) and Implicit (Backward) Euler method, Classical second-order Runge-Kutta (RK2) method (Heun’s or Improved method), Third-order (RK3) Fourth-order (RK...

The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which used to solve Falkner-Skan equation. nonlinear differential equation converting a system equations solved using Mathematica®12, approximate solutions are obtained. efficiency these methods was studied by calculating maximum error remainder ( ), it found that their increases as increases. Moreover...

In this study, we considered a model for novel COVID-19 consisting on five classes, namely S, susceptible; E, exposed; I, infected; V, vaccinated; and R, recovered. We derived the expression basic reproductive rate R0 studied disease-free endemic equilibrium as well local global stability. addition, extended nonstandard finite difference scheme to simulate our using some real data. Moreover, ke...

This study focuses on the solution of rotationally symmetric Rossler attractor by using adaptive predictor–corrector algorithm (Apc-ABM-method) and fractional Laplace decomposition method (ρ-Laplace DM). Furthermore, a comparison between proposed methods Runge–Kutta Fourth Order (RK4) is made. It discovered that are effective yield solutions identical to approximate produced other methods. Ther...

In immersed interface methods, solids in a fluid are represented by singular forces in the Navier–Stokes equations, and flow jump conditions induced by the singular forces directly enter into numerical schemes. This paper focuses on the implementation of an immersed interface method for simulating fluid–solid interaction in 3D. The method employs the MAC scheme for the spatial discretization, t...

An analysis is reported here for three-time level integration methods following the global spectral analysis (GSA) described in High Accuracy Computing Methods , T.K. Sengupta, Cambridge Univ. Press, USA. The focus is on the second order Adams–Bashforth (AB2) and the extrapolation in time (EXT2) methods. Careful distinction is made for the first time step at t = 0 by either Euler forward or fou...

Solving a non-linear differential equation most times is difficult and requires some technicalities. Many semi-analytical methods were derived in literature to provide series solution problem, with each method giving level of accuracy when compared their equivalent exact (or numerical case does not exist). Thus, system ordinary equations (ODEs) arising from formulated Susceptible-Infected-Quara...

In this investigation, some analytical solutions to both conserved and non-conserved rotational pendulum systems are reported. The exact solution the oscillator (unforced, undamped oscillator), is derived in form of a Jacobi elliptical function. Moreover, an approximate for case obtained trigonometric A comparison between examined. approximations oscillators including unforced, damped forced, o...

In this study, both the ansatz and averaging methods are carried out for analyzing complex Duffing oscillators including undamped/conserved oscillator (CDO) damped/unconserved CDO to obtain some approximate analytical solutions. To analyze conserved CDO, it is reduced two decoupled oscillators. After that, exact solution of employed derive an approximation in terms Jacobi elliptic function. dam...

In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the oscillator (I) (FDCDO (I)) FDCDO (II), investigated by using effective analytical numerical approaches. For approximation, models of FDCDOs reduced to decoupled standard (FDDOs). After that, both ansatz method Krylov–Bogoliubov–Mitropolsky (KBM) app...