Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative
In this paper, an initial-boundary value problem for a one-dimensional linear time-dependent fractional Schrödinger pseudoparabolic partial differential equation with Caputo derivative of order α∈0,1 is being considered. Two strong numerical methods are employed to acquire the solutions to the probl...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7113205 |
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| _version_ | 1849308576526368768 |
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| author | Mahmut Modanli Bushra Bajjah |
| author_facet | Mahmut Modanli Bushra Bajjah |
| author_sort | Mahmut Modanli |
| collection | DOAJ |
| description | In this paper, an initial-boundary value problem for a one-dimensional linear time-dependent fractional Schrödinger pseudoparabolic partial differential equation with Caputo derivative of order α∈0,1 is being considered. Two strong numerical methods are employed to acquire the solutions to the problem. The first method used is the double Laplace decomposition method where closed-form solutions are obtained for any α∈0,1. As the second method, the implicit finite difference scheme is applied to obtain the approximate solutions. To clarify the performance of these two methods, numerical results are presented. The stability of the problem is also investigated. |
| format | Article |
| id | doaj-art-1aa6afd6452f4d1c92f09e48d9ed5c83 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1aa6afd6452f4d1c92f09e48d9ed5c832025-08-20T03:54:24ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/71132057113205Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo DerivativeMahmut Modanli0Bushra Bajjah1Harran University, Faculty of Arts and Sciences, Department of Mathematics, 63300 Sanliurfa, TurkeyThamar University, Faculty of Applied Sciences, Department of Mathematics, Dhamar, YemenIn this paper, an initial-boundary value problem for a one-dimensional linear time-dependent fractional Schrödinger pseudoparabolic partial differential equation with Caputo derivative of order α∈0,1 is being considered. Two strong numerical methods are employed to acquire the solutions to the problem. The first method used is the double Laplace decomposition method where closed-form solutions are obtained for any α∈0,1. As the second method, the implicit finite difference scheme is applied to obtain the approximate solutions. To clarify the performance of these two methods, numerical results are presented. The stability of the problem is also investigated.http://dx.doi.org/10.1155/2021/7113205 |
| spellingShingle | Mahmut Modanli Bushra Bajjah Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative Journal of Mathematics |
| title | Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative |
| title_full | Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative |
| title_fullStr | Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative |
| title_full_unstemmed | Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative |
| title_short | Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative |
| title_sort | double laplace decomposition method and finite difference method of time fractional schrodinger pseudoparabolic partial differential equation with caputo derivative |
| url | http://dx.doi.org/10.1155/2021/7113205 |
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