TY - JOUR
ID - 16547
TI - Adaptive-grid technique for the numerical solution of a class of fractional boundary-value-problems
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Maji, Sandip
AU - Natesan, Srinivasan
AD - Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India.
Y1 - 2024
PY - 2024
VL - 12
IS - 2
SP - 338
EP - 349
KW - fractional differential equation
KW - Riemann-Liouville-Caputo fractional derivative
KW - Shooting method
KW - Stability estimate
DO - 10.22034/cmde.2023.55266.2296
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_16547.html
L1 - https://cmde.tabrizu.ac.ir/article_16547_603eebf1d379ea7f1966da4792be224e.pdf
ER -