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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Numerical Solution of Modified Time Fractional Burgers' Equation Utilizing a Novel Cubic B-Splines Collocation Technique

Journal of Applied Nonlinear Dynamics 15(2) (2026) 349--360 | DOI:10.5890/JAND.2026.06.007

Kuruku Ankith, Sreenivasulu Ballem

Department of Mathematics, Central University of Karnataka-585367, India

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Abstract

The present study applies functions of new cubic B-splines to compute numerical solutions for the modified time fractional Burgers equation using the $\theta $-weighted scheme, employing time fractional derivative using the Caputo fractional order derivative. The finite difference method is employed for the discretization of time, while the cubic B-splines are used for spatial discretization. The quasi-linearization technique was employed to linearize the nonlinear term in the given fractional differential equation. The effectiveness of the proposed method was tested on one specific problem, with the impact of viscosity $\mu$ and parameter $\beta\in(0,1]$ depicted through 2D and 3D graphs. An algorithm is used to explain the suggested approach, the von Neumann technique was employed to analyze the stability of the suggested scheme, which was found to be unconditionally stable. The second-order convergence of the scheme in both spatial and temporal directions has also been discussed and confirmed. To evaluate the accuracy of the proposed scheme, error norms have been calculated and examined.

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