A new efficient technique for solving two-point boundary value problems for integro-differential equations

Singh, Randhir; Nelakanti, Gnaneshwar; Kumar, Jitendra

doi:10.1007/s10910-014-0363-8

Cited by 6 publications

(3 citation statements)

References 38 publications

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“…Many problems in chemical engineering are described by means of ordinary differential equations or partial differential equations with initial or boundary conditions [19,20]. In the numerical section, we transform, by means of divided differences, a nonlinear boundary value problem with non-Dirichlet conditions in a nonlinear system, whose solution is an approximation of the solution of the boundary value problem in a set of discrete points of the domain.…”

Section: Introductionmentioning

confidence: 99%

CMMSE2017: On two classes of fourth- and seventh-order vectorial methods with stable behavior

2017

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Section: Introductionmentioning

confidence: 99%

CMMSE2017: On two classes of fourth- and seventh-order vectorial methods with stable behavior

2017

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“…In many branches of applied mathematics, chemistry, physics and engineering, efficient solvers of nonlinear problems are needed: in mass and heat transfer within porous catalyst particles, some boundary value problems for integro-differential equations appear that, after accurate discretization, Adomian decomposition or other techniques, yield to a nonlinear system of equations (see, for example [1] and [2]). Also nonlinear reactiondiffusion equations arise in autocatalytic chemical reactions (see [3]) or the analysis of the electronic structure of the hydrogen-atom in strong magnetic fields can be treated numerically, [4], by using iterative procedures for solving nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

A new fourth-order family for solving nonlinear problems and its dynamics

et al. 2014

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In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made in order to choose those elements of the family with better conditions of stability. These results are checked by solving the nonlinear system that arises from the partial differential equation of molecular interaction.

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“…Comparison of the absolute error of Example 4.1 by using new method and modified ADM decomposition method in the paper[7] 表 1. 模型(4.1)中用新方法和改进的 ADM 分解方法得到的绝对误差比较[7] …”

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confidence: 99%

RKM and ADM Decomposition Method for Solving a Class of Two-Order Integral-Differential Equations

廉雪娇¹,

吕学琴²

2016

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In this paper, we use RKM and ADM decomposition method to solve a class of second-order boundary value problems for integral-differential equations. This method avoids the series solution of the equation with unknown parameters. At the same time, the problem of convergence analysis is also given in this paper. Additionally, some numerical examples are presented to demonstrate the rationality of this algorithm.

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A new efficient technique for solving two-point boundary value problems for integro-differential equations

Cited by 6 publications

References 38 publications

CMMSE2017: On two classes of fourth- and seventh-order vectorial methods with stable behavior

CMMSE2017: On two classes of fourth- and seventh-order vectorial methods with stable behavior

A new fourth-order family for solving nonlinear problems and its dynamics

RKM and ADM Decomposition Method for Solving a Class of Two-Order Integral-Differential Equations

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