We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Adaptive-grid technique for the numerical solution of a class of fractional boundary-value-problems.
- Authors
Maji, Sandip; Natesan, Srinivasan
- Abstract
In this study, we numerically solve a class of two-point boundary-value-problems with a Riemann-Liouville-Caputo fractional derivative, where the solution might contain a weak singularity. Using the shooting technique based on the secant iterative approach, the boundary value problem is first transformed into an initial value problem, and the initial value problem is then converted into an analogous integral equation. The functions contained in the fractional integral are finally approximated using linear interpolation. An adaptive mesh is produced by equidistributing a monitor function in order to capture the singularity of the solution. A modified Gronwall inequality is used to establish the stability of the numerical scheme. To show the effectiveness of the suggested approach over an equidistributed grid, two numerical examples are provided.
- Subjects
BOUNDARY value problems; FRACTIONAL calculus; MATHEMATICAL singularities; ITERATIVE methods (Mathematics); INTEGRAL equations
- Publication
Computational Methods for Differential Equations, 2024, Vol 12, Issue 2, p338
- ISSN
2345-3982
- Publication type
Article
- DOI
10.22034/CMDE.2023.55266.2296