A fast-converging iterative scheme for solving a system of Lane–Emden equations arising in catalytic diffusion reactions

Madduri, Harshita; Roul, Pradip

doi:10.1007/s10910-018-0964-8

Cited by 30 publications

(14 citation statements)

References 15 publications

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“…the fact that such equations model a reaction-diffusion process (see e.g. [13,23,37] and references therein). It appears that analytical solitons of such problems are useful in the optimization of this process (see e.g.…”

Section: Motivationsmentioning

confidence: 99%

Existence and properties of solutions for boundary value problems based on the nonlinear reactor dynamics

Orpel

2020

J Math Chem

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We deal with the existence of positive solutions for the following class of nonlinear equation u �� (t) + Au � (t) + g(t, u(t), v(t)) = 0 a.e. in (0, 1), with boundary conditions u � (0) = 0 , u � (1) + Au(1) = 0 , where v is a functional parameter. The form of the problem is associated with the classical model described by Markus and Amundson. We show the existence of at least one positive solution of this problem and discuss its properties. Moreover we describe conditions that guarantee the continuous dependence of solution on parameter v also in the case of the lack of the uniqueness of a solution. The results are based on the clasical fixed point methods. Our approach allows us to consider both sub and superlinear nonlinearities which may be singular with respect to the first variable.

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Section: Motivationsmentioning

confidence: 99%

Existence and properties of solutions for boundary value problems based on the nonlinear reactor dynamics

Orpel

2020

J Math Chem

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“…It plays a fundamental role in explaining the structures of stars and planets [1]. It can be used to model equilibrium density distribution of polytrophic isothermal gas and diffusion process [2][3]. The singularity at origin makes it of fundamental importance modeling of cluster of galaxies.…”

Section: Introductionmentioning

confidence: 99%

Improved Numerical Computation to Solve Lane-Emden type Equations

2021

IJATCSE

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Lane-Emden equation is also of fundamental importance in mathematical physics, celestial mechanics,and computer science. It can be used to describe stellar structures, equilibrium density distribution in polytrophicisothermal gas, thermal behavior in mutual attraction of its molecules. An improved numerical method is developed for solving Lane-Emden type differential equations. The method is based on power series solutions of differential equations and Maclaurin series expansion. A python program is written to carry out numerical calculations. Five examples are solved and shown in this paper, the solutions obtained by the program are compared with the exact solutions of differential equation, an excellent agreement is found between them. The present method improves runtime.

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“…Equation (1.1) models the catalytic diffusion reactions [6]. There are several numerical methods as well as analytical methods to deal with these types of equations in recent years [6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

First order smooth composite Chebyshev finite difference method for solving coupled Lane-Emden problem in catalytic diffusion reactions

Aydinlik¹,

Kirisb²

2021

match

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A new effective technique based on Chebyshev Finite Difference Method is introduced. First order smoothness of the approximation polynomial at the end points of each sub-interval is imposed in addition to the continuity condition. Both round-off and truncation error analyses are given besides the convergence analysis. Coupled Lane Emden boundary value problem in Catalytic Diffusion Reactions is investigated by using presented method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results than the others.

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A fast-converging iterative scheme for solving a system of Lane–Emden equations arising in catalytic diffusion reactions

Cited by 30 publications

References 15 publications

Existence and properties of solutions for boundary value problems based on the nonlinear reactor dynamics

Existence and properties of solutions for boundary value problems based on the nonlinear reactor dynamics

Improved Numerical Computation to Solve Lane-Emden type Equations

First order smooth composite Chebyshev finite difference method for solving coupled Lane-Emden problem in catalytic diffusion reactions

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