We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A Novel Quintic B-Spline Technique for Numerical Solutions of the Fourth-Order Singular Singularly-Perturbed Problems.
- Authors
Yousaf, Muhammad Zain; Srivastava, Hari Mohan; Abbas, Muhammad; Nazir, Tahir; Mohammed, Pshtiwan Othman; Vivas-Cortez, Miguel; Chorfi, Nejmeddine
- 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.
- Subjects
QUINTIC equations; BOUNDARY value problems; NONLINEAR equations; INITIAL value problems; NUCLEAR reactions; QUASILINEARIZATION
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 10, p1929
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15101929