Abstract The new rational a -polynomials are used to solve the Falkner-Skan equation. These polynomials equipped with an auxiliary parameter. approximated solution equation is obtained by unknown coefficients. To find coefficients and parameter contained in polynomials, collocation method Chebyshev-Gauss points used. numerical examples show efficiency of this method.

Methanogenesis in cold marine sediments is a globally important process leading to methane hydrate deposits, cold seeps, physical instability of sediment, and atmospheric methane emissions. We employed a multidisciplinary approach that combined culture-dependent and -independent analyses with geochemical measurements in the sediments of Skan Bay, Alaska (53 degrees N, 167 degrees W), to investi...

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...

We propose an iterative method for solving the Falkner-Skan equation. The method provides approximate analytical solutions which consist of coefficients of the previous iterate solution. By some examples, we show that the presented method with a small number of iterations is competitive with the existing method such as Adomian decomposition method. Furthermore, to improve the accuracy of the pr...

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solv...

Based on a new approximation method, namely pseudospectral method, a solution for the three order nonlinear ordinary differential laminar boundary layer Falkner-Skan equation has been obtained on the semi-infinite domain. The proposed approach is equipped by the orthogonal Hermite functions that have perfect properties to achieve this goal. This method solves the problem on the semi-infinite do...

A numerical technique is presented for the solution of Falkner-Skan equation. The nonlinear ordinary differential equation is solved using Chebyshev cardinal functions. The method have been derived by first truncating the semi-infinite physical domain of the problem to a finite domain and expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the oper...