This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involv...

This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution differential equations (FDEs). We construct explicit and implicit FORK FDEs by using Caputo generalized Taylor series formula. Due to dependence derivatives on fixed base point, in proposed method, we had modify right-hand side given equation all steps methods. Some coeffici...

The numerical behavior of two implicit time-marching methods is investigated in solving two-dimensional unsteady compressible flows. The two methods are the second-order multistep backward differencing formula and the fourth-order multistage explicit first stage, single-diagonal coefficient, diagonally implicit Runge-Kutta scheme. A Newton-Krylov method is used to solve the nonlinear problem ar...

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...

We implement two different algorithms for computing numerically the direct Zakharov–Shabat eigenvalue problem on the infinite line. The first algorithm replaces the potential in the eigenvalue problem by a piecewise-constant approximation, which allows one to solve analytically the corresponding ordinary differential equation. The resulting algorithm is of second order in the step size. The sec...

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi‐ step integration methods. The coefficients are reverse engineered based on samples from a target function and its derivative used for training. The Runge‐Kutta schemes are tra...

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 ...

In this paper, semi-analytical method for asymmetrical eccentrically stiffened FGM cylindrical shells under external pressure and surrounded by a linear and non-linear elastic foundation is presented. The proposed linear model is based on two parameter elastic foundation Winkler and Pasternak. According to the von Karman nonlinear equations and the classical plate theory of shells, strain-displ...

The present paper deals with the effects of Ohmic dissipative Casson fluid flow over a stretching sheet in the presence of aligned magnetic field. The present phenomenon also includes the interaction of thermal radiation and velocity slip. The governing boundary layer equations are transformed into a set of ordinary differential equations using the similarity transformations. The dimensionless ...