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 L2-norm. Numerical results highlight the high accuracy and efficiency of the proposed strategy and clarify the theoretical prediction.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference46 articles.
1. Decay Properties for the Numerical Solutions of a Partial Differential Equation with Memory
2. A general theory of heat conduction with finite wave speeds
3. Theory of Viscoelasticity: An Introduction;Christensen,2012
4. Mathematical Analysis of Viscoelastic Flows
5. Exponential decay of the viscoelastic Euler-Bernoulli equation with a nonlocal dissipation in general domains;Cavalcanti;Differ. Inte. Equ.,2004