Doubly singular boundary value problems with derivative dependent source function: A fast‐converging iterative approach

Roul, Pradip

doi:10.1002/mma.5351

Cited by 13 publications

(4 citation statements)

References 31 publications

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“…Roul [126] claims to derive that a fast-converging recursive scheme is presented to approximate the solution of a class of derivative dependent doubly singular boundary value problems (94) subject to (97) or (98). The original problem is reformulated as an equivalent integral equation and then was solved by an improved HAM with a parameter that accelerates the convergence.…”

Section: Numerical Results When the Nonlinear Term Is F (X Y Py )mentioning

confidence: 99%

A Review on a Class of Second Order Nonlinear Singular BVPs

et al. 2020

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Several real-life problems are modeled by nonlinear singular differential equations. In this article, we study a class of nonlinear singular differential equations, explore its various aspects, and provide a detailed literature survey. Nonlinear singular differential equations are not easy to solve and their exact solution does not exist in most cases. Since the exact solution does not exist, it is natural to look for the existence of the analytical solution and numerical solution. In this survey, we focus on both aspects of nonlinear singular boundary value problems (SBVPs) and cover different analytical and numerical techniques which are developed to deal with a class of nonlinear singular differential equations − ( p ( x ) y ′ ( x ) ) ′ = q ( x ) f ( x , y , p y ′ ) for x ∈ ( 0 , b ) , subject to suitable initial and boundary conditions. The monotone iterative technique has also been briefed as it gained a lot of attention during the last two decades and it has been merged with most of the other existing techniques. A list of SBVPs is also provided which will be of great help to researchers working in this area.

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Section: Numerical Results When the Nonlinear Term Is F (X Y Py )mentioning

confidence: 99%

A Review on a Class of Second Order Nonlinear Singular BVPs

et al. 2020

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“…In 2014, Singh et al [26] discussed the Adomian decomposition technique to solve an original utilizing Green's function. In 2018, Roul [32] presented an improved normal homotopy analysis method to solve derivative-dependent SBVPs, and in 2019, Roul et al [33] discussed quintic spline interpolation. In 2020, Shahni et al [34] established an approximate solution for Emden-Fowler-type SBVPs with derivative dependence using Bernstein polynomials.…”

Section: Introductionmentioning

confidence: 99%

Collocation Technique Based on Chebyshev Polynomials to Solve Emden–Fowler-Type Singular Boundary Value Problems with Derivative Dependence

Kumari,

Singh,

Gupta

2024

Mathematics

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In this work, an innovative technique is presented to solve Emden–Fowler-type singular boundary value problems (SBVPs) with derivative dependence. These types of problems have significant applications in applied mathematics and astrophysics. Initially, the differential equation is transformed into a Fredholm integral equation, which is then converted into a system of nonlinear equations using the collocation technique based on Chebyshev polynomials. Subsequently, an iterative numerical approach, such as Newton’s method, is employed on the system of nonlinear equations to obtain an approximate solution. Error analysis is included to assess the accuracy of the obtained solutions and provide insights into the reliability of the numerical results. Furthermore, we graphically compare the residual errors of the current method to the previously established method for various examples.

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“…In recent years, nonlinear singular boundary value problems (SBVPs) have been extensively studied in the literature 1‐5 . A wide variety of physical phenomena, such as the thermal behaviour of a spherical cloud of gas, oxygen diffusion in a cell, isothermal gas sphere, electrohydrodynamic flow of a fluid in a cylinder, and thermal explosion are modelled by SBVPs, see previous studies 6‐10 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical method based on exponential B‐spline basis functions for solving a class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

Roul

Kumari

Goura

2020

Math Methods in App Sciences

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In this paper, we develop a numerical scheme to approximate the solution of a general class of nonlinear singular boundary value problems (SBVPs) subject to Neumann and Robin boundary conditions. The original differential equation has a singularity at the point x=0, which is removed via L'Hospital's law with an assumption about the derivative of the solution at the point x=0. An exponential B‐spline collocation approach is then constructed to solve the resulting boundary value problem. Convergence analysis of the method is discussed. Numerical examples are provided to illustrate the applicability and efficiency of the method. Our results are compared with those obtained by other three numerical methods such as uniform mesh cubic B‐spline collocation (UCS) method, nonstandard finite difference method, and finite difference method based on Chawla's identity.

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Doubly singular boundary value problems with derivative dependent source function: A fast‐converging iterative approach

Cited by 13 publications

References 31 publications

A Review on a Class of Second Order Nonlinear Singular BVPs

A Review on a Class of Second Order Nonlinear Singular BVPs

Collocation Technique Based on Chebyshev Polynomials to Solve Emden–Fowler-Type Singular Boundary Value Problems with Derivative Dependence

An efficient numerical method based on exponential B‐spline basis functions for solving a class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

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