Numerical solution of general order Emden-Fowler-type Pantograph delay differential equations

The present study introduces the Haar wavelet method, which utilizes collocation points to approximate solutions to the Emden-Fowler Pantograph delay differential equations (PDDEs) of general order. This semi-analytic method requires the transformation of the original differential equation into a sy...

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Bibliographic Details
Published inDemonstratio mathematica Vol. 57; no. 1; pp. 63 - 43
Main Authors Albalawi, Kholoud Saad, Kumar, Ashish, Alqahtani, Badr Saad, Goswami, Pranay
Format Journal Article
LanguageEnglish
Published De Gruyter 09.08.2024
Subjects
65L60
65T60
Emden-Fowler-type equations
Haar wavelet method
Pantograph delay differential equations
Primary 34A34
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Summary:The present study introduces the Haar wavelet method, which utilizes collocation points to approximate solutions to the Emden-Fowler Pantograph delay differential equations (PDDEs) of general order. This semi-analytic method requires the transformation of the original differential equation into a system of nonlinear differential equations, which is then solved to determine the Haar coefficients. The method’s application to fourth-, fifth-, and sixth-order PDDEs is discussed, along with an examination of convergence that involves the determination of an upper bound and the formulation of the rate of convergence for the method. Numerical simulations and error tables are presented to demonstrate the effectiveness and precision of this approach. The error tables clearly illustrate that the method’s accuracy improves progressively with increasing resolution.
ISSN:2391-4661
2391-4661
DOI:10.1515/dema-2024-0023