A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations

Кутнів, М. В.; Datsko, Bohdan; Kunynets, Andrii; Włoch, Andrzej

doi:10.1016/j.apnum.2019.09.006

Cited by 9 publications

(2 citation statements)

References 16 publications

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“…It was claimed that the presented sixth-order stage order two L stable 6(5) pair explicit first stage, single diagonally implicit RK method was the first of its kind. An approach was given in Kutniv et al 5 to construct high-order step numerical methods for solving initial value problems on a finite domain. A transformation was given that reduced the problem on semi-infinite interval and then used the finite irregular grid on a semi-infinite interval.…”

Section: Introductionmentioning

confidence: 99%

A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

Nawaz

Abodayeh

Arif

et al. 2021

Advances in Mechanical Engineering

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A two-stage third-order numerical scheme is proposed for solving ordinary differential equations. The scheme is explicit and implicit type in two stages. First, the stability region of the scheme is found when it is applied to the linear equation. Further, the stability conditions of the scheme are found using a linearized homogenous set of differential equations. This set of equations is obtained by applying transformations on the governing equations of heat and mass transfer of incompressible, laminar, steady, two-dimensional, and non-Newtonian power-law fluid flows over a stretching sheet with effects of thermal radiations and chemical reaction. The proposed scheme with an iterative method is employed in two different forms called linearized and non-linearized. But it is found that the non-linearized approach performs better than the linearized one when residuals are compared through plots. Additionally, the proposed scheme is compared to the second-order central finite difference method for second-order non-linear differential equations and the Keller-Box/trapezoidal method for a linear differential equation. It is determined that the proposed scheme is more effective and computationally less expensive than the standard/classical finite difference methods. Moreover, the impact of magnetic parameter, radiation parameter, modified Prandtl and Schmidt numbers for power-law fluid, and chemical reaction rate parameter on velocity, temperature, and concentration profiles are displayed through graphs and discussed. The power-law fluid’s heat and mass transfer simulations are also carried out with varying flow behavior index, sheet velocity, and mass diffusivity. We hoped that this effort would serve as a guide for investigators tasked with resolving unresolved issues in the field of enclosures used in industry and engineering.

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Section: Introductionmentioning

confidence: 99%

A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

Nawaz

Abodayeh

Arif

et al. 2021

Advances in Mechanical Engineering

View full text Add to dashboard Cite

show abstract

“…equations and introducing many methods to solve this type of equations [1][2][3][4][5]. One of those methods is Adomian Decomposition method (ADM) [6][7][8][9][10][11][12], which is a numerical method that was introduced by George Adomian in 1980s [13,14] to solve different equations.…”

Section: Introductionmentioning

confidence: 99%

Application of Adomian Decomposition Method to Solving Higher Order Singular Value Problems for Ordinary Differential Equations

Hasan¹,

Alaqel²

2020

AJPAS

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Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs

Datsko,

Kutniv

2024

Numer Algor

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A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations

Cited by 9 publications

References 16 publications

A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

Application of Adomian Decomposition Method to Solving Higher Order Singular Value Problems for Ordinary Differential Equations

Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs

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