Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays
Abstract In this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03107-9 |
| _version_ | 1819170051498967040 |
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| author | Seyyedeh Roodabeh Moosavi Noori Nasir Taghizadeh |
| author_facet | Seyyedeh Roodabeh Moosavi Noori Nasir Taghizadeh |
| author_sort | Seyyedeh Roodabeh Moosavi Noori |
| collection | DOAJ |
| description | Abstract In this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided. |
| first_indexed | 2024-12-22T19:29:15Z |
| format | Article |
| id | doaj.art-685aef3c2cfd4ca79da4952fa09c61c3 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T19:29:15Z |
| publishDate | 2020-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-685aef3c2cfd4ca79da4952fa09c61c32022-12-21T18:15:09ZengSpringerOpenAdvances in Difference Equations1687-18472020-11-012020112510.1186/s13662-020-03107-9Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delaysSeyyedeh Roodabeh Moosavi Noori0Nasir Taghizadeh1Department of Pure Mathematics, Faculty of Mathematical Sciences, University of GuilanDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of GuilanAbstract In this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.http://link.springer.com/article/10.1186/s13662-020-03107-9Modified differential transform methodLaplace transformPadé approximationPantograph equationExact solutions |
| spellingShingle | Seyyedeh Roodabeh Moosavi Noori Nasir Taghizadeh Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays Advances in Difference Equations Modified differential transform method Laplace transform Padé approximation Pantograph equation Exact solutions |
| title | Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays |
| title_full | Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays |
| title_fullStr | Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays |
| title_full_unstemmed | Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays |
| title_short | Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays |
| title_sort | modified differential transform method for solving linear and nonlinear pantograph type of differential and volterra integro differential equations with proportional delays |
| topic | Modified differential transform method Laplace transform Padé approximation Pantograph equation Exact solutions |
| url | http://link.springer.com/article/10.1186/s13662-020-03107-9 |
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