A novel quintic B-spline technique for numerical solutions of the fourth-order singular singularly-perturbed problems
Date
2023
Authors
Yousaf, Muhammad Zain
Srivastava, Hari Mohan
Abbas, Muhammad
Nazir, Tahir
Mohammed, Pshtiwan Othman
Vivas-Cortez, Miguel
Chorfi, Nejmeddine
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
Singular singularly-perturbed problems (SSPPs) are a powerful mathematical tool for modelling a variety of real phenomena, such as nuclear reactions, heat explosions, mechanics, and hydrodynamics. In this paper, the numerical solutions to fourth-order singular singularly-perturbed boundary and initial value problems are presented using a novel quintic B-spline (QBS) approximation approach. This method uses a quasi-linearization approach to solve SSPNL initial/boundary value problems. And the non-linear problems are transformed into a sequence of linear problems by applying the quasi-linearization approach. The QBS functions produce more accurate results when compared to other existing approaches because of their local support, symmetry, and partition of unity features. This method can be applied to immediately solve the SSPPs without reducing the order in which they are presented. It has been demonstrated that the suggested numerical approach converges uniformly over the whole domain. The proposed approach is implemented on a few problems to validate the scheme. The computational results are compared, and they illustrate that the proposed approach performs better.
Description
Keywords
singular singularly-perturbed non-linear initial/boundary value problems, uniform convergence, fourth-order Emden–fowler type equation, QBS function, fourth-order BVP and IVP
Citation
Yousaf, M. Z., Srivastava, H. M., Abbas, M., Nazir, T., Mohammed, P. O., Vivas-Cortez, M., & Chorfi, N. (2023). A novel quintic B-spline technique for numerical solutions of the fourth-order singular singularly-perturbed problems. Symmetry, 15(10), 1929. https://doi.org/10.3390/sym15101929