# A High-Order B-Spline Collocation Method For Solving Nonlinear Singular Boundary Value Problems Arising In Engineering And Applied Science

Kiran Thula, Pradip Roul

Published 2018 · Mathematics

In this paper, a high-order B-spline collocation method on a uniform mesh is presented for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions: $$\begin{aligned} (p(x)y')'= & {} p(x)f(x,y), \quad 0

This paper references

10.1016/0022-5193(76)90071-0

Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics.

S. Lin (1976)

10.1016/0096-3003(89)90053-2

Pointwise solution bounds for a class of singular diffusion problems in physiology

N. S. Asaithambi (1989)

10.1016/J.CAM.2003.09.053

On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology

R. K. Pandey (2004)

10.1007/BF01390712

Spline finite difference methods for singular two point boundary value problems

S. K. Iyengar (1986)

10.1016/0022-5193(78)90270-9

A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics.

D. L. McElwain (1978)

10.1016/j.mcm.2010.04.009

A novel approach for the solution of a class of singular boundary value problems arising in physiology

Suheil A. Khuri (2010)

10.1016/S0377-0427(01)00537-4

A three-point finite difference method for a class of singular two-point boundary value problems

M. Kumar (2002)

10.1016/J.CAM.2008.06.005

On the convergence of a fourth-order method for a class of singular boundary value problems

R. K. Pandey (2009)

10.1007/BF01933711

Orderh2 method for a singular two-point boundary value problem

M. H. Chawla (1986)

10.1080/00207160211935

On the Convergence of a Spline Method for Singular Two Point Boundary Value Problems Arising in Physiology

Rajeev K. Pandey (2002)

10.1016/J.CHAOS.2007.06.007

B-spline solution of non-linear singular boundary value problems arising in physiology

H. Caglar (2009)

10.1080/00207168808803650

A new spline method for singular two-point boundary value problems

M. H. Chawla (1988)

10.1007/BF01934697

A fourth order method for a singular two-point boundary value problem

M. H. Chawla (1988)

10.1142/S0219876213500527

NUMERICAL SOLUTION FOR THE NONLINEAR EMDEN–FOWLER TYPE EQUATIONS BY A FOURTH-ORDER ADAPTIVE METHOD

S. A. Khuri (2014)

10.1016/j.amc.2007.01.002

Cubic spline polynomial for non-linear singular two-point boundary value problems

A. Kanth (2007)

10.1080/00207160701600168

Differential quadrature method (DQM) for a class of singular two-point boundary value problems

Ugur Yücel (2009)

10.1016/S0022-5193(75)80131-7

The distribution of heat sources in the human head: a theoretical consideration.

U. Flesch (1975)

10.1080/00207160008804927

A note on a finite difference method for a class of singular boundary value problems in physiology

R. Pandey (2000)

10.1016/j.compchemeng.2011.08.008

A note on the solution of singular boundary value problems arising in engineering and applied sciences: Use of OHAM

Mohammad Danish (2012)

10.1080/00207169708804603

A finite difference method for a class Of singular two point boundary value problems arising in physiology

R. Pandey (1997)

10.1006/jmaa.1997.5320

On a Class of Regular Singular Two Point Boundary Value Problems

R. K. Pandey (1997)

10.1016/0022-5193(80)90250-7

The distribution of heat sources in the human head--theoretical considerations.

B. F. Gray (1980)

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Pradip Roul (2019)

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Pradip Roul (2020)

10.1016/j.amc.2019.124727

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Pradip Roul (2020)

10.1007/978-3-030-21080-9_10

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Ali Ümit Keskin (2019)

10.1016/j.amc.2019.01.001

A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

Pradip Roul (2019)

10.1007/978-3-030-21080-9_9

Approximating Solutions of BVPs Using Cubic B-Splines

Ali Ümit Keskin (2019)

10.1007/s10910-020-01105-6

A sixth order optimal B-spline collocation method for solving Bratu’s problem

Pradip Roul (2020)

10.1002/MMA.5351

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

Pradip Roul (2019)

10.1016/j.cam.2020.112881

A sixth order numerical method and its convergence for generalized Black-Scholes PDE

Pradip Roul (2020)

10.1016/J.APNUM.2019.06.016

A new high order numerical approach for a class of nonlinear derivative dependent singular boundary value problems

Pradip Roul (2019)