Single-term Walsh series method for solving Volterra's population model

Sepehrian, Behnam

doi:10.14419/ijamr.v3i4.3431

Cited by 9 publications

(2 citation statements)

References 14 publications

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“…There are many approximate and numerical solutions for Volterra's population model, we name a few [18,20,21,22,23,24,25,26,27,28,29,30,31,32]. We can solve Eq.…”

Section: The Model Of Volterra Populationmentioning

confidence: 99%

A multiple-scale power series method for solving nonlinear ordinary differential equations

Liu¹,

Kuo²,

Jhao³

2016

Communications in Numerical Analysis

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The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales R k in the power term (t/R k ) k is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.

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“…There are many approximate and numerical solutions for Volterra's population model, we name a few [18,20,21,22,23,24,25,26,27,28,29,30,31,32]. We can solve Eq.…”

Section: The Model Of Volterra Populationmentioning

confidence: 99%

A multiple-scale power series method for solving nonlinear ordinary differential equations

Liu¹,

Kuo²,

Jhao³

2016

Communications in Numerical Analysis

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“…In [18] a STWS method for nonlinear Volterra-Hammerstein equations is introduced and in [4], Balakumar and Murugusan developed the method for linear systems of Volterra integral equations. Also, Sepehrian introduced a STWS method for solving Volterra's population model in [17].…”

Section: Introductionmentioning

confidence: 99%

A New Method for Solving Nonlinear Volterra-Hammerstein Integral Equations Via Single-Term Walsh Series

Sepehrian

Razzaghi

2020

MACO

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In this article, the properties of single-term Walsh series are presented and utilized for solving the nonlinear Volterra-Hammerstein integral equations of second kind. The interval [0, 1) is divided to m equal subintervals, m is a positive integer number. The midpoint of each subinterval is chosen as a suitable collocation point. By the method the computations of integral equations reduce into some nonlinear algebraic equations. The method is computationally attractive, and gives a continuous approximate solution. An analysis for the convergence of method is presented. The efficiency and accuracy of the method are demonstrated through illustrative examples. Some comparisons are made with the existing results.

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Numerical Solutions of Non-Linear System of Higher Order Volterra Integro-Differential Equations using Generalized STWS Technique

Sekar

Murugesan

2017

Differ Equ Dyn Syst

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Single-term Walsh series method for solving Volterra's population model

Cited by 9 publications

References 14 publications

A multiple-scale power series method for solving nonlinear ordinary differential equations

A multiple-scale power series method for solving nonlinear ordinary differential equations

A New Method for Solving Nonlinear Volterra-Hammerstein Integral Equations Via Single-Term Walsh Series

Numerical Solutions of Non-Linear System of Higher Order Volterra Integro-Differential Equations using Generalized STWS Technique

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