Multiple solutions of mixed convection in a porous medium on semi-infinite interval using pseudo-spectral collocation method

Reproducing kernel method for singular multi-point boundary value problems

“…10, 11 and 12 represent ℏ-curves and the horizontal line illustrates the range of convergence for Eq. (27). Further, the efficiency of proposed scheme is Table 3 and it clear that the proposed method is very accurate.…”

On the Analytic Solution for a Steady Magnetohydrodynamic Equation

“…As mentioned in the previous section, the obtained series solutions by the LADM (17) has not the correct behaviour at infinity according to the boundary condition f (∞) = 1, and this power series solution cannot be directly applied. To overcome this problem, here the obtained power series (17) will be approximated by a rational function, called Padé approximation.…”

“…To get the missing value γ, we will employ the infinity boundary condition f (∞) = 1. For this purpose, f (τ) of the series solution given by (17) After computing the missing value γ, an accurate approximated semi-analytical solution for the governing problem can be given as Padé approximation of the series solution given by (17). Now, notice that based on the presented results in [32], the uniqueness and convergence solution of (8) (8) and (9) in the two following cases:…”

“…We know that, when [S/N](τ) is exactly a Padé approximation of the series solution f (τ) given by (17)…”

A new spectral meshless radial point interpolation (SMRPI) method: A well-behaved alternative to the meshless weak forms

“…This method is accomplished successfully by using Chebyshev polynomials approximation and generating approximations for the higher order derivatives through successive differentiation of the approximate solution, the readers are referred to [47,48] (and references therein). In spectral meshless radial point interpolation (SMRPI) method [49], the point interpolation method with the help of radial basis functions is proposed to construct shape functions which have Kronecker delta function property and are used as basis function in the frame of SMRPI.…”