Approximation approach for backward stochastic Volterra integral equations
In this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. We used Newton's technique to solve a particular BSVIE by employing block...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Mathematical Modelling and Control |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2024031 |
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| author | Kutorzi Edwin Yao Mahvish Samar Yufeng Shi |
| author_facet | Kutorzi Edwin Yao Mahvish Samar Yufeng Shi |
| author_sort | Kutorzi Edwin Yao |
| collection | DOAJ |
| description | In this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. We used Newton's technique to solve a particular BSVIE by employing block pulse functions (BPFs) and the related stochastic operational matrix of integration. Additionally, we developed considerations for Lipschitz and linear growth, along with linearity conditions, to illustrate error and convergence analysis. We compared the solutions we obtain the values of exact and approximate solutions at selected points with a defined absolute error. The computations were performed using MATLAB R2018a. |
| format | Article |
| id | doaj-art-17373203d48742c28f065d4ea3fe0eb1 |
| institution | Kabale University |
| issn | 2767-8946 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj-art-17373203d48742c28f065d4ea3fe0eb12025-01-24T01:02:16ZengAIMS PressMathematical Modelling and Control2767-89462024-11-014439039910.3934/mmc.2024031Approximation approach for backward stochastic Volterra integral equationsKutorzi Edwin Yao0Mahvish Samar1Yufeng Shi2Institute for Financial Studies, Shandong University, Ji'nan 250100, ChinaSchool of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, ChinaInstitute for Financial Studies, Shandong University, Ji'nan 250100, ChinaIn this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. We used Newton's technique to solve a particular BSVIE by employing block pulse functions (BPFs) and the related stochastic operational matrix of integration. Additionally, we developed considerations for Lipschitz and linear growth, along with linearity conditions, to illustrate error and convergence analysis. We compared the solutions we obtain the values of exact and approximate solutions at selected points with a defined absolute error. The computations were performed using MATLAB R2018a.https://www.aimspress.com/article/doi/10.3934/mmc.2024031bsviesbsdesbpfsoperational matrixcollocation approximation |
| spellingShingle | Kutorzi Edwin Yao Mahvish Samar Yufeng Shi Approximation approach for backward stochastic Volterra integral equations Mathematical Modelling and Control bsvies bsdes bpfs operational matrix collocation approximation |
| title | Approximation approach for backward stochastic Volterra integral equations |
| title_full | Approximation approach for backward stochastic Volterra integral equations |
| title_fullStr | Approximation approach for backward stochastic Volterra integral equations |
| title_full_unstemmed | Approximation approach for backward stochastic Volterra integral equations |
| title_short | Approximation approach for backward stochastic Volterra integral equations |
| title_sort | approximation approach for backward stochastic volterra integral equations |
| topic | bsvies bsdes bpfs operational matrix collocation approximation |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2024031 |
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