Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel

Qiong Huang, Omid Nikan and Zakieh Avazzadeh ()
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Qiong Huang: School of Pharmacy, Henan University of Chinese Medicine, Zhengzhou 450046, China
Omid Nikan: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
Zakieh Avazzadeh: Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa

Mathematics, 2022, vol. 10, issue 18, 1-18

Abstract: This paper studies an alternating direction implicit orthogonal spline collocation (ADIOSC) technique for calculating the numerical solution of the hyperbolic integrodifferential problem with a weakly singular kernel in the two-dimensional domain. The integral term is approximated with the help of the second-order fractional quadrature formula introduced by Lubich. The stability and convergence analysis of the proposed strategy are proven in L 2 -norm. Numerical results highlight the high accuracy and efficiency of the proposed strategy and clarify the theoretical prediction.

Keywords: hyperbolic integrodifferential equation; orthogonal spline collocation method; alternating direction implicit method; error analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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