Application of Euler Matrix Method for Solving Linear and a Class of Nonlinear Fredholm Integro-Differential Equations

Mirzaee, Farshid; Bimesl, Saeed

doi:10.1007/s00009-014-0391-4

Cited by 20 publications

(5 citation statements)

References 30 publications

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“…We focus now in integral equations of Fredholm-type, different numerical methods have been developed to approximate their solution, for example, Fredholm-type integral equations [18,21,24], Volterra-Fredholm integral equations [9,17] and nonlinear Fredholm integro-differential equations [16] can be considered.…”

Section: Introductionmentioning

confidence: 99%

A Fixed-Point Type Result for Some Non-Differentiable Fredholm Integral Equations

Hernández-Verón,

Singh,

Martínez

et al. 2024

Mathematical Modelling and Analysis

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In this paper, we present a new fixed-point result to draw conclusions about the existence and uniqueness of the solution for a nonlinear Fredholm integral equation of the second kind with non-differentiable Nemytskii operator. To do this, we will transform the problem of locating a fixed point for an integral operator into the problem of locating a solution of an integral equation. Thus, assuming conditions on the Nemytskii operator, we will obtain a global convergence domain for the solution of the considered integral equation, taking for this a uniparametric family of derivativefree iterative processes with quadratic convergence. This result provides us a new fixed-point result for the integral operator considered.

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Section: Introductionmentioning

confidence: 99%

A Fixed-Point Type Result for Some Non-Differentiable Fredholm Integral Equations

Hernández-Verón,

Singh,

Martínez

et al. 2024

Mathematical Modelling and Analysis

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“…In 1986, Zhou 28 first introduced a semi-analytical method named differential transform method (DTM) in which the solution is chosen as a truncated Maclaurin series and applied to analyze linear and nonlinear electric circuit problems. Then some authors applied the DTM [29][30][31][32][33][34] to solve linear and nonlinear differential equations. But such truncated series solution does not nicely exhibit the periodic behavior which is characteristic of oscillator equations.…”

Section: Introductionmentioning

confidence: 99%

An approximation technique for solving nonlinear oscillators

Huq,

Hasan,

Alam

2023

Journal of Low Frequency Noise, Vibration and Active Control

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Recently, an approximation technique was presented for solving strong nonlinear oscillators modeled by second-order differential equations. Due to the arising of an algebraic complicity, the method fails to determine suitable solution of some important nonlinear problems such as quadratic oscillator, cubical Duffing oscillator of softening springs, and pendulum equation. However, suitable solutions of these oscillators are found by rearranging only an algebraic equation related to amplitude and frequency. The determination of solutions is simpler than the original version.

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“…In this sense, Keller–Segel problems from mathematical biology may involve nonlinear diffusion and external actions. Moreover, there are recent development in numerical techniques for solving various models arising in applied sciences and engineering, such as Volterra integro-differential equations of pantograph-delay type, 15 Telegraph equations, 16 linear complex differential equations, 17 systems of high-order Fredholm integro-differential equations, 18,19 nonlinear fractional Volterra integro-differential equations, 20 systems of high-order linear differential–difference equations, 21 system of linear Volterra integral equations with variable coefficients, 22 second-order hyperbolic partial differential equation, 23 nonlinear stochastic Itô-Volterra integral equations, 24 and nonlocal reaction chemotaxis model. 25…”

Section: Introductionmentioning

confidence: 99%

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

Abdelrahman

Alkhidhr

Mohamed

2022

Journal of Low Frequency Noise, Vibration and Active Control

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We consider the isothermal Euler model with non-vacuum initial data. We extract the Riemann invariants of the isothermal Euler model, which admits vital applications. We also design the modified Rusanov (mR) scheme to solve the isothermal Euler model. This scheme consists of two steps, the first step of the scheme depends on a local parameter allowing to control diffusion. The second stage recovers conservation equation. This technique is a straightforward to implement and precise. We compare this scheme with the Rusanov scheme via three numerical examples. This numerical study verifies the efficiency of the mR scheme. Finally, the mR scheme can be used to solve many other models in applied science.

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Application of Euler Matrix Method for Solving Linear and a Class of Nonlinear Fredholm Integro-Differential Equations

Cited by 20 publications

References 30 publications

A Fixed-Point Type Result for Some Non-Differentiable Fredholm Integral Equations

A Fixed-Point Type Result for Some Non-Differentiable Fredholm Integral Equations

An approximation technique for solving nonlinear oscillators

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

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