Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

Mishra, Vinod; Rani, Dimple

doi:10.1051/matecconf/20165705001

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…The study is implemented on three model examples with exact solutions by taking different values for N, and the computational results are presented in the Tables (1)(2)(3)(4)(5)(6)(7)(8). The results obtained by the present method are compared with the results of Gemechis and Tasfaye [4], Vinod and Dimple [5], Fateme and Esmaile [6] and shows betterment. Furthermore, from the Tables (1-5) it is significant that all of the absolute errors decrease rapidly as h decreases, which in turn shows the convergence of the computed solution.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, some researchers have been tried to find the approximate solution of first order nonlinear ordinary differential equations. For example; Gashu and Habtamu [3] considered the comparison of higher order Taylor's method and fifth order Runge-Kutta method; Gemechis and Tesfaye [4] presented fourth order Runge-Kutta for solving quadratic Riccati differential equations; Vinod and Dimple [5] presented Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations;…”

Section: Introductionmentioning

confidence: 99%

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Fifth Order Predictor-Corrector Method for Solving Quadratic Riccati Differential Equations

Kiltu¹,

Roba²,

Hailu³

2017

International Journal of Engineering &Amp; Applied Sciences

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fifth Order Predictor-Corrector Method for Solving Quadratic Riccati Differential Equations

Kiltu¹,

Roba²,

Hailu³

2017

International Journal of Engineering &Amp; Applied Sciences

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“…It was used very effectively on a wide range of physical models of partial differential equations, such as Burger's equation is a non linear PDE of second order, which have many applications in sciences and technology. The numerical solutions of three dimensional Burger's equation and Riccati differential equations by using LADM have been discussed in [4,5]. LADM is also used for the numerical solution of a special mathematical model for vector born diseases [6].…”

Section: Introductionmentioning

confidence: 99%

Laplace Adomian Decomposition Method for Multi Dimensional Time Fractional Model of Navier-Stokes Equation

et al. 2019

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In this research paper, a hybrid method called Laplace Adomian Decomposition Method (LADM) is used for the analytical solution of the system of time fractional Navier-Stokes equation. The solution of this system can be obtained with the help of Maple software, which provide LADM algorithm for the given problem. Moreover, the results of the proposed method are compared with the exact solution of the problems, which has confirmed, that as the terms of the series increases the approximate solutions are convergent to the exact solution of each problem. The accuracy of the method is examined with help of some examples. The LADM, results have shown that, the proposed method has higher rate of convergence as compare to ADM and HPM. ). Although it is considered an old topic, but for the last few decade, fractional calculus is launched as an important topic by the scientists and researchers [10,11].The Navier-Stokes equation is known as Newton second Law for fluid substance, has been derived in 1822 by Claude Louis Navier and Gabriel Stokes. Navier-Stokes equation is an important model to describe many physical phenomena in applied sciences. This model have the capacity of modelling weather, ocean current, water flow in pipes and air flow around a wing. A very special case was considered, which has established the relationship between pressure and external forces acting on the fluid to the responses of fluid flow [12]. The Navier-Stock equation is also used to derive the connection between viscous fluid with rigid bodies and considered a best tool in the field of thermohydraulics, meteorology, petroleum industry, plasma physics and technology [13].Several mathematicians have applied different techniques for the solution of Navier-Stock equation. Among these methods, Kumar et al. have implemented modified Laplace decomposition method for the analytical solution of fractional Navier-Stokes equation [14] coupled method is the combination of He-Laplace transform (HLT) and Fractional Complex Transform (FCT) is used to solve Navier-Stock equation [15]. Fractional Reduced Differential Transformation Method (FRDM) is also implemented for the numerical solution of time fractional Navier-Stock equation [16], see also [17]. Definitions and Preliminaries ConceptsIn this unit, among few definitions of fractional calculus, presented in the article due to Riemann Liouville, Grunwald Letnikov, Caputo, etc., first folks simple descriptions and introductions are reconsidered, which we want to comprehend our education.

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On $$(1+\sqrt{2})$$ convergence-based Newton–Raphson method for approximate solution of singular value Lane-Emden differential equation via modified Laplace Adomian decomposition technique

Sahu

Jena

2023

Int. j. inf. tecnol.

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Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

Cited by 5 publications

References 18 publications

Fifth Order Predictor-Corrector Method for Solving Quadratic Riccati Differential Equations

Fifth Order Predictor-Corrector Method for Solving Quadratic Riccati Differential Equations

Laplace Adomian Decomposition Method for Multi Dimensional Time Fractional Model of Navier-Stokes Equation

On $$(1+\sqrt{2})$$ convergence-based Newton–Raphson method for approximate solution of singular value Lane-Emden differential equation via modified Laplace Adomian decomposition technique

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