Approximations to linear Klein–Gordon Equations using Haar wavelet
In this research article, two Haar wavelet collocation methods (HWCMs) (namely one dimensional HWCM and two dimensional HWCM) are adapted to approximate linear homogeneous and linear non-homogeneous Klein–Gordon equations. The results obtained from both methods are compared with exact solutions. Mor...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-12-01
|
| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447921001295 |
| _version_ | 1828953356573343744 |
|---|---|
| author | Sana Ikram Sidra Saleem Malik Zawwar Hussain |
| author_facet | Sana Ikram Sidra Saleem Malik Zawwar Hussain |
| author_sort | Sana Ikram |
| collection | DOAJ |
| description | In this research article, two Haar wavelet collocation methods (HWCMs) (namely one dimensional HWCM and two dimensional HWCM) are adapted to approximate linear homogeneous and linear non-homogeneous Klein–Gordon equations. The results obtained from both methods are compared with exact solutions. Moreover, both of the methods are also compared together, that indicates much better performance of two dimensional Haar wavelet collocation method (2D HWCM) in a small number of collocation points. |
| first_indexed | 2024-12-14T07:09:37Z |
| format | Article |
| id | doaj.art-f4c664b45c9b40d99ad17b7ddab74d72 |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-12-14T07:09:37Z |
| publishDate | 2021-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-f4c664b45c9b40d99ad17b7ddab74d722022-12-21T23:12:00ZengElsevierAin Shams Engineering Journal2090-44792021-12-0112439873995Approximations to linear Klein–Gordon Equations using Haar waveletSana Ikram0Sidra Saleem1Malik Zawwar Hussain2Department of Mathematics, University of the Punjab, Lahore, PakistanCorresponding author. Tel./fax: +92-(0) 99231444.; Department of Mathematics, University of the Punjab, Lahore, PakistanDepartment of Mathematics, University of the Punjab, Lahore, PakistanIn this research article, two Haar wavelet collocation methods (HWCMs) (namely one dimensional HWCM and two dimensional HWCM) are adapted to approximate linear homogeneous and linear non-homogeneous Klein–Gordon equations. The results obtained from both methods are compared with exact solutions. Moreover, both of the methods are also compared together, that indicates much better performance of two dimensional Haar wavelet collocation method (2D HWCM) in a small number of collocation points.http://www.sciencedirect.com/science/article/pii/S209044792100129565M0665M1265M70 |
| spellingShingle | Sana Ikram Sidra Saleem Malik Zawwar Hussain Approximations to linear Klein–Gordon Equations using Haar wavelet Ain Shams Engineering Journal 65M06 65M12 65M70 |
| title | Approximations to linear Klein–Gordon Equations using Haar wavelet |
| title_full | Approximations to linear Klein–Gordon Equations using Haar wavelet |
| title_fullStr | Approximations to linear Klein–Gordon Equations using Haar wavelet |
| title_full_unstemmed | Approximations to linear Klein–Gordon Equations using Haar wavelet |
| title_short | Approximations to linear Klein–Gordon Equations using Haar wavelet |
| title_sort | approximations to linear klein gordon equations using haar wavelet |
| topic | 65M06 65M12 65M70 |
| url | http://www.sciencedirect.com/science/article/pii/S2090447921001295 |
| work_keys_str_mv | AT sanaikram approximationstolinearkleingordonequationsusinghaarwavelet AT sidrasaleem approximationstolinearkleingordonequationsusinghaarwavelet AT malikzawwarhussain approximationstolinearkleingordonequationsusinghaarwavelet |