A Green's function-based computationally efficient approach for solving a kind of nonlocal BVPs

Document Type : Research Paper


Department of Mathematics, JUIT Solan, Waknaghat--$173234$, Himachal Pradesh, India.


This study attempts to find approximate numerical solutions for a kind of second-order nonlinear differential problem subject to some Dirichlet and mixed-type nonlocal (specifically three-point) boundary conditions, appearing in various realistic physical phenomena, such as bridge design, control theory, thermal explosion, thermostat model, and the theory of elastic stability. The proposed approach offers an efficient and rapid solution for addressing the inherent complexity of nonlinear differential problems with nonlocal boundary conditions. Picard's iterative technique and quasilinearization method are the basis for the proposed coupled iterative methodology. In order to convert nonlinear boundary value problems to linearized form, the quasilinearization approach (with convergence controller parameters) is implemented. Making use of the Picard's iteration method with the assistance of Green's function, an equivalent integral representation for the linearized problems is derived. Discussion is also had over the proposed method's convergence analysis. In order to determine its efficiency and effectiveness, the coupled iterative technique is tested on some numerical examples. Results are also compared with the existing techniques and documented (in terms of absolute errors) to validate the accuracy and precision of the proposed iterative technique.


Main Subjects

Articles in Press, Accepted Manuscript
Available Online from 23 April 2024
  • Receive Date: 25 August 2023
  • Revise Date: 07 January 2024
  • Accept Date: 09 February 2024