Cubic spline solutions of the ninth order linear and non-linear boundary value problems

Xiao Zhong Zhang; Aasma Khalid; Mustafa Inc; Akmal Rehan; Kottakkaran Sooppy Nisar; M. S. Osman

doi:10.1016/j.aej.2022.05.003

Cubic spline solutions of the ninth order linear and non-linear boundary value problems

Xiao Zhong Zhang
, Aasma Khalid
, Mustafa Inc
, Akmal Rehan
, Kottakkaran Sooppy Nisar
, M. S. Osman

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

A lot of numerical formulations of physical phenomena contain 9^th-order BVPs. The presented probe intends to consider the spline solutions of the 9^th-order boundary value problems using Cubic B Spline(CBS). Ninth order boundary value problems arise in the study of laminar viscous flow in a semi-porous channel, astrophysics, hydrodynamic & hydro-magnetic stability. The derived technique is exceptionally useful and is appropriate for such kinds of linear and non-linear boundary value problems. Cubic B Spline(CBS) is successfully applied to mathematical models. The outcomes are contrasted to those presented in the literature, revealing that the introduced technique leads to an advisable estimation of the exact solution.

Original language	English
Pages (from-to)	11635-11649
Number of pages	15
Journal	Alexandria Engineering Journal
Volume	61
Issue number	12
DOIs	https://doi.org/10.1016/j.aej.2022.05.003
State	Published - Dec 2022

Keywords

Absolute errors
Boundary value problems
Central finite difference approximations
Cubic B-spline

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10.1016/j.aej.2022.05.003

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title = "Cubic spline solutions of the ninth order linear and non-linear boundary value problems",

abstract = "A lot of numerical formulations of physical phenomena contain 9th-order BVPs. The presented probe intends to consider the spline solutions of the 9th-order boundary value problems using Cubic B Spline(CBS). Ninth order boundary value problems arise in the study of laminar viscous flow in a semi-porous channel, astrophysics, hydrodynamic \& hydro-magnetic stability. The derived technique is exceptionally useful and is appropriate for such kinds of linear and non-linear boundary value problems. Cubic B Spline(CBS) is successfully applied to mathematical models. The outcomes are contrasted to those presented in the literature, revealing that the introduced technique leads to an advisable estimation of the exact solution.",

keywords = "Absolute errors, Boundary value problems, Central finite difference approximations, Cubic B-spline",

author = "Zhang, \{Xiao Zhong\} and Aasma Khalid and Mustafa Inc and Akmal Rehan and Nisar, \{Kottakkaran Sooppy\} and Osman, \{M. S.\}",

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year = "2022",

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doi = "10.1016/j.aej.2022.05.003",

language = "English",

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TY - JOUR

T1 - Cubic spline solutions of the ninth order linear and non-linear boundary value problems

AU - Zhang, Xiao Zhong

AU - Khalid, Aasma

AU - Inc, Mustafa

AU - Rehan, Akmal

AU - Nisar, Kottakkaran Sooppy

AU - Osman, M. S.

PY - 2022/12

Y1 - 2022/12

N2 - A lot of numerical formulations of physical phenomena contain 9th-order BVPs. The presented probe intends to consider the spline solutions of the 9th-order boundary value problems using Cubic B Spline(CBS). Ninth order boundary value problems arise in the study of laminar viscous flow in a semi-porous channel, astrophysics, hydrodynamic & hydro-magnetic stability. The derived technique is exceptionally useful and is appropriate for such kinds of linear and non-linear boundary value problems. Cubic B Spline(CBS) is successfully applied to mathematical models. The outcomes are contrasted to those presented in the literature, revealing that the introduced technique leads to an advisable estimation of the exact solution.

AB - A lot of numerical formulations of physical phenomena contain 9th-order BVPs. The presented probe intends to consider the spline solutions of the 9th-order boundary value problems using Cubic B Spline(CBS). Ninth order boundary value problems arise in the study of laminar viscous flow in a semi-porous channel, astrophysics, hydrodynamic & hydro-magnetic stability. The derived technique is exceptionally useful and is appropriate for such kinds of linear and non-linear boundary value problems. Cubic B Spline(CBS) is successfully applied to mathematical models. The outcomes are contrasted to those presented in the literature, revealing that the introduced technique leads to an advisable estimation of the exact solution.

KW - Absolute errors

KW - Boundary value problems

KW - Central finite difference approximations

KW - Cubic B-spline

UR - https://www.scopus.com/pages/publications/85131251187

U2 - 10.1016/j.aej.2022.05.003

DO - 10.1016/j.aej.2022.05.003

M3 - Article

AN - SCOPUS:85131251187

SN - 1110-0168

VL - 61

SP - 11635

EP - 11649

JO - Alexandria Engineering Journal

JF - Alexandria Engineering Journal

IS - 12

ER -

Cubic spline solutions of the ninth order linear and non-linear boundary value problems

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Keywords

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