An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations

In this research study, a novel computational algorithm for solving a second-order singular functional differential equation as a generalization of the well-known Lane–Emden and differential-difference equations is presented by using the Bessel bases. This technique depends on transforming the probl...

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Main Authors: Mohammad Izadi, Hari M. Srivastava, Waleed Adel
Format: Article
Language:English
Published: MDPI AG 2022-03-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/11/3/133
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author Mohammad Izadi
Hari M. Srivastava
Waleed Adel
author_facet Mohammad Izadi
Hari M. Srivastava
Waleed Adel
author_sort Mohammad Izadi
collection DOAJ
description In this research study, a novel computational algorithm for solving a second-order singular functional differential equation as a generalization of the well-known Lane–Emden and differential-difference equations is presented by using the Bessel bases. This technique depends on transforming the problem into a system of algebraic equations and by solving this system the unknown Bessel coefficients are determined and the solution will be known. The method is tested on several test examples and proves to provide accurate results as compared to other existing methods from the literature. The simplicity and robustness of the proposed technique drive us to investigate more of their applications to several similar problems in the future.
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spelling doaj.art-e3dee348050746c0b70996b787c185182023-11-30T20:50:22ZengMDPI AGAxioms2075-16802022-03-0111313310.3390/axioms11030133An Effective Approximation Algorithm for Second-Order Singular Functional Differential EquationsMohammad Izadi0Hari M. Srivastava1Waleed Adel2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, IranDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, EgyptIn this research study, a novel computational algorithm for solving a second-order singular functional differential equation as a generalization of the well-known Lane–Emden and differential-difference equations is presented by using the Bessel bases. This technique depends on transforming the problem into a system of algebraic equations and by solving this system the unknown Bessel coefficients are determined and the solution will be known. The method is tested on several test examples and proves to provide accurate results as compared to other existing methods from the literature. The simplicity and robustness of the proposed technique drive us to investigate more of their applications to several similar problems in the future.https://www.mdpi.com/2075-1680/11/3/133Bessel polynomialscollocation pointsdifferential-difference equationfunctional differential equationsingular Lane–Emden type equation
spellingShingle Mohammad Izadi
Hari M. Srivastava
Waleed Adel
An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations
Axioms
Bessel polynomials
collocation points
differential-difference equation
functional differential equation
singular Lane–Emden type equation
title An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations
title_full An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations
title_fullStr An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations
title_full_unstemmed An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations
title_short An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations
title_sort effective approximation algorithm for second order singular functional differential equations
topic Bessel polynomials
collocation points
differential-difference equation
functional differential equation
singular Lane–Emden type equation
url https://www.mdpi.com/2075-1680/11/3/133
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