Solutions of initial and boundary value problems using invariant curves

Khudija Bibi; Khudija Bibi

doi:10.3934/math.20241072

AIMS Mathematics

2024, Volume 9, Issue 8: 22057-22066. doi: 10.3934/math.20241072

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Solutions of initial and boundary value problems using invariant curves

Khudija Bibi ^,

Department of Mathematics and Statistics, Faculty of Sciences, International Islamic University Islamabad, Pakistan

Received: 26 January 2024 Revised: 31 March 2024 Accepted: 11 April 2024 Published: 15 July 2024
MSC : 22E70, 34B60, 34C45

The purpose of this study is to investigate the solutions of initial and boundary value problems of ordinary differential equations by employing Lie symmetry generators. In this investigation, it shown that invariant curves, which obtained by symmetry generators, also be utilized to find solutions to initial and boundary value problems. A method, involving invariant curves, presented to find solutions to initial and boundary value problems. Solutions to many linear and nonlinear initial and boundary value problems discussed by applying the proposed method.
- initial and boundary value problems,
- Lie symmetries,
- invariant curves,
- solutions
Citation: Khudija Bibi. Solutions of initial and boundary value problems using invariant curves[J]. AIMS Mathematics, 2024, 9(8): 22057-22066. doi: 10.3934/math.20241072

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Abstract

The purpose of this study is to investigate the solutions of initial and boundary value problems of ordinary differential equations by employing Lie symmetry generators. In this investigation, it shown that invariant curves, which obtained by symmetry generators, also be utilized to find solutions to initial and boundary value problems. A method, involving invariant curves, presented to find solutions to initial and boundary value problems. Solutions to many linear and nonlinear initial and boundary value problems discussed by applying the proposed method.

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