An Effective Approach Based on Generalized Bernstein Basis Functions for the System of Fourth-Order Initial Value Problems for an Arbitrary Interval Article Swipe
Muhammad Abdul Basit
,
Komal Shahnaz
,
Rida Malik
,
Samsul Ariffin Abdul Karim
,
Faheem Khan
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/math11143076
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/math11143076
The system of ordinary differential equations has many uses in contemporary mathematics and engineering. Finding the numerical solution to a system of ordinary differential equations for any arbitrary interval is very appealing to researchers. The numerical solution of a system of fourth-order ordinary differential equations on any finite interval [a,b] is found in this work using a symmetric Bernstein approximation. This technique is based on the operational matrices of Bernstein polynomials for solving the system of fourth-order ODEs. First, using Chebyshev collocation nodes, a generalised approximation of the system of ordinary differential equations is discretized into a system of linear algebraic equations that can be solved using any standard rule, such as Gaussian elimination. We obtain the numerical solution in the form of a polynomial after obtaining the unknowns. The Hyers–Ulam and Hyers–Ulam–Rassias stability analyses are provided to demonstrate that the proposed technique is stable under certain conditions. The results of numerical experiments using the proposed technique are plotted in figures to demonstrate the accuracy of the specified approach. The results show that the suggested Bernstein approximation method for any interval is quick and effective.
Related Topics
Concepts
Mathematics
Bernstein polynomial
Collocation method
Interval (graph theory)
Ordinary differential equation
Numerical stability
Applied mathematics
Collocation (remote sensing)
Discretization
Differential equation
Initial value problem
Orthogonal collocation
Numerical analysis
Algebraic equation
Mathematical analysis
Nonlinear system
Computer science
Machine learning
Combinatorics
Quantum mechanics
Physics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/math11143076
- https://www.mdpi.com/2227-7390/11/14/3076/pdf?version=1689174826
- OA Status
- gold
- References
- 25
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4384202573
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4384202573Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/math11143076Digital Object Identifier
- Title
-
An Effective Approach Based on Generalized Bernstein Basis Functions for the System of Fourth-Order Initial Value Problems for an Arbitrary IntervalWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-07-12Full publication date if available
- Authors
-
Muhammad Abdul Basit, Komal Shahnaz, Rida Malik, Samsul Ariffin Abdul Karim, Faheem KhanList of authors in order
- Landing page
-
https://doi.org/10.3390/math11143076Publisher landing page
- PDF URL
-
https://www.mdpi.com/2227-7390/11/14/3076/pdf?version=1689174826Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://www.mdpi.com/2227-7390/11/14/3076/pdf?version=1689174826Direct OA link when available
- Concepts
-
Mathematics, Bernstein polynomial, Collocation method, Interval (graph theory), Ordinary differential equation, Numerical stability, Applied mathematics, Collocation (remote sensing), Discretization, Differential equation, Initial value problem, Orthogonal collocation, Numerical analysis, Algebraic equation, Mathematical analysis, Nonlinear system, Computer science, Machine learning, Combinatorics, Quantum mechanics, PhysicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- References (count)
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25Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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