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...
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| Format: | Article |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3390 |
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| author | Qiong Huang Omid Nikan Zakieh Avazzadeh |
| author_facet | Qiong Huang Omid Nikan Zakieh Avazzadeh |
| author_sort | Qiong Huang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T23:15:06Z |
| format | Article |
| id | doaj.art-d3074ad4da684903827f086c7e8fd05b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:06Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d3074ad4da684903827f086c7e8fd05b2023-11-23T17:37:56ZengMDPI AGMathematics2227-73902022-09-011018339010.3390/math10183390Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular KernelQiong Huang0Omid Nikan1Zakieh Avazzadeh2School of Pharmacy, Henan University of Chinese Medicine, Zhengzhou 450046, ChinaSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, IranDepartment of Mathematical Sciences, University of South Africa, Florida 0003, South AfricaThis 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.https://www.mdpi.com/2227-7390/10/18/3390hyperbolic integrodifferential equationorthogonal spline collocation methodalternating direction implicit methoderror analysis |
| spellingShingle | Qiong Huang Omid Nikan Zakieh Avazzadeh Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel Mathematics hyperbolic integrodifferential equation orthogonal spline collocation method alternating direction implicit method error analysis |
| title | Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel |
| title_full | Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel |
| title_fullStr | Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel |
| title_full_unstemmed | Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel |
| title_short | Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel |
| title_sort | numerical analysis of alternating direction implicit orthogonal spline collocation scheme for the hyperbolic integrodifferential equation with a weakly singular kernel |
| topic | hyperbolic integrodifferential equation orthogonal spline collocation method alternating direction implicit method error analysis |
| url | https://www.mdpi.com/2227-7390/10/18/3390 |
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