Numerical solution of non-linear Bratu-type boundary value problems via quintic B-spline collocation method

Ram Kishun Lodhi; Saud Fahad Aldosary; Kottakkaran Sooppy Nisar; Ateq Alsaadi; Ram Kishun Lodhi; Saud Fahad Aldosary; Kottakkaran Sooppy Nisar; Ateq Alsaadi

doi:10.3934/math.2022405

AIMS Mathematics

2022, Volume 7, Issue 4: 7257-7273. doi: 10.3934/math.2022405

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Numerical solution of non-linear Bratu-type boundary value problems via quintic B-spline collocation method

1.
Department of Applied Science, Symbiosis Institute of Technology, Symbiosis International University, Pune-412115, India
2.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 10 December 2021 Revised: 19 January 2022 Accepted: 21 January 2022 Published: 10 February 2022
MSC : 34A34, 65L10

This study presents a quintic B-spline collocation method (QBSCM) for finding the numerical solution of non-linear Bratu-type boundary value problems (BVPs). The error analysis of the QBSCM is studied, and it provides fourth-order convergence results. QBSCM is applied on two numerical examples to exhibit the proficiency and order of convergence. Obtain results of the QBSCM are compared with other existing methods available in the literature.
- quintic B-spline collocation method,
- Bratu-type problems,
- error analysis,
- order of convergence
Citation: Ram Kishun Lodhi, Saud Fahad Aldosary, Kottakkaran Sooppy Nisar, Ateq Alsaadi. Numerical solution of non-linear Bratu-type boundary value problems via quintic B-spline collocation method[J]. AIMS Mathematics, 2022, 7(4): 7257-7273. doi: 10.3934/math.2022405

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Abstract

This study presents a quintic B-spline collocation method (QBSCM) for finding the numerical solution of non-linear Bratu-type boundary value problems (BVPs). The error analysis of the QBSCM is studied, and it provides fourth-order convergence results. QBSCM is applied on two numerical examples to exhibit the proficiency and order of convergence. Obtain results of the QBSCM are compared with other existing methods available in the literature.

References

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