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Maji, Sandip, Natesan, Srinivasan. (1402). Adaptive-grid technique for the numerical solution of a class of fractional boundary-value-problems. سامانه مدیریت نشریات علمی, 12(2), 338-349. doi: 10.22034/cmde.2023.55266.2296
Sandip Maji; Srinivasan Natesan. "Adaptive-grid technique for the numerical solution of a class of fractional boundary-value-problems". سامانه مدیریت نشریات علمی, 12, 2, 1402, 338-349. doi: 10.22034/cmde.2023.55266.2296
Maji, Sandip, Natesan, Srinivasan. (1402). 'Adaptive-grid technique for the numerical solution of a class of fractional boundary-value-problems', سامانه مدیریت نشریات علمی, 12(2), pp. 338-349. doi: 10.22034/cmde.2023.55266.2296
Maji, Sandip, Natesan, Srinivasan. Adaptive-grid technique for the numerical solution of a class of fractional boundary-value-problems. سامانه مدیریت نشریات علمی, 1402; 12(2): 338-349. doi: 10.22034/cmde.2023.55266.2296

Adaptive-grid technique for the numerical solution of a class of fractional boundary-value-problems

Computational Methods for Differential Equations
مقاله 10، دوره 12، شماره 2، خرداد 2024، صفحه 338-349    اصل مقاله (425.13 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55266.2296
نویسندگان
Sandip Maji؛ Srinivasan Natesan*
Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India.
چکیده
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.
کلیدواژه‌ها
Fractional differential equation؛ Riemann-Liouville-Caputo fractional derivative؛ Shooting method؛ Stability estimate
مراجع
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