Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel
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 t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/18/3390 |
| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mn>2</mn></msup></semantics></math></inline-formula>-norm. Numerical results highlight the high accuracy and efficiency of the proposed strategy and clarify the theoretical prediction. |
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| ISSN: | 2227-7390 |