A fixed point approach for finding approximate solutions to second order non-instantaneous impulsive abstract differential equations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909090215624704 |
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| author | Ansari, Shahin Malik, Muslim Ali, Javid |
| author_facet | Ansari, Shahin Malik, Muslim Ali, Javid |
| contents | This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection operator. We investigate the connection between the approximate solution and exact solution, and the question of convergence. Moreover, we define the Faedo-Galerkin(F-G) approximations and prove the existence and convergence results. The results are obtained by using the theory of cosine functions, Banach fixed point theorem and fractional power of closed linear operators. At last, an example of abstract formulation is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02445 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A fixed point approach for finding approximate solutions to second order non-instantaneous impulsive abstract differential equations Ansari, Shahin Malik, Muslim Ali, Javid Numerical Analysis 34A45, 47D09, 34G20, 34A37. 34A45, 47D09, 34G20, 34A37. 34A45, 47D09, 34G20, 34A37 This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection operator. We investigate the connection between the approximate solution and exact solution, and the question of convergence. Moreover, we define the Faedo-Galerkin(F-G) approximations and prove the existence and convergence results. The results are obtained by using the theory of cosine functions, Banach fixed point theorem and fractional power of closed linear operators. At last, an example of abstract formulation is provided. |
| title | A fixed point approach for finding approximate solutions to second order non-instantaneous impulsive abstract differential equations |
| topic | Numerical Analysis 34A45, 47D09, 34G20, 34A37. 34A45, 47D09, 34G20, 34A37. 34A45, 47D09, 34G20, 34A37 |
| url | https://arxiv.org/abs/2309.02445 |