Modified hybrid B-spline estimation based on spatial regulator tensor network for burger equation with nonlinear fractional calculus

Baiheng Cao, Xuedong Wu, Yaonan Wang and Zhiyu Zhu

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 220, issue C, 253-275

Abstract: In this paper, a modified hybrid B-spline approximation based on spatial regulator tensor network (MHBA-SRTN) is proposed for solving the application and the feasibility problems of fractional calculus-based Burger equation. The main innovation points include: (1) a dual singular kernel based fractional derivative operator is employed on the Burger’s equation with external force term to analyze the solutions and properties under perturbation condition for further realism simulation; (2) a modified hybrid B-spline basis function and its corresponding topological tensor network structure are further proposed to solve the provided Burger’s equation with more favorable approximation accuracy and solution uniqueness; (3) the tensor network transformed the hybrid B-spline construction process into the tensor solving with the introduced spatially regulated tensor network decomposition for a more robust solution procedure; (4) an acceleration approach for decomposition process is introduced to significantly reduce its computational and storage complexity. Extensive experiments are also carried out to verify the performance of MHBA-SRTN.

Keywords: B-Spline; Dual Singular Kernel Fractional Derivative Operator; Tensor Rank; Tensor Network Decomposition; Spatial Restriction (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:220:y:2024:i:c:p:253-275

DOI: 10.1016/j.matcom.2024.01.006

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