Numerical Solutions of a Class of Fourth-Order Non-Linear Equations for Singular Boundary Value Problems

Document Type : Research Paper

Authors
Biswajit Pandit 1
Pratikshya Manini 2
B.R. Priyanka 3
Ravi P. Agarwal 4
1 Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, Itanagar, 791109, India
2 Center of Data Sciences, Siksha ‘O’ Anusandhan, ITER College, Odisha, 751030, India
3 Department of Mathematics, APS College of Engineering, Bengaluru, 560082, India
4 Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
10.22055/jacm.2026.48985.5644
Abstract
In this article, we investigate the numerical approximation of solutions to a class of fourth-order singular boundary value problems subject to various boundary conditions. The difficulty of the problem stems from its nonlinear, non-self-adjoint, and singular nature, along with the absence of closed-form solutions, which complicates analytical treatment. Moreover, the presence of dual solutions further challenges the construction of accurate approximations using standard discrete methods. To overcome these issues, we develop an iterative technique with the help of governing problem and the boundary conditions. We then show that the resulting numerical approximations converge to the exact solution. Several numerical examples are presented to demonstrate the accuracy, effectiveness, and broad applicability of the proposed method.
Keywords
Fourth Order
Singular Boundary Value Problems
Non-Self-Adjoint Operators
Iterative Method
Subjects

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Journal of Applied and Computational Mechanics
Volume 12, Issue 3
Summer 2026
Pages 1288-1303