Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets
A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The prop...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-01-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/28/abstr.html |
| _version_ | 1818130129612701696 |
|---|---|
| author | Prakash Kumar Sahu Santanu Saha Ray |
| author_facet | Prakash Kumar Sahu Santanu Saha Ray |
| author_sort | Prakash Kumar Sahu |
| collection | DOAJ |
| description | A numerical method based on Legendre multi-wavelets is applied for solving
Lane-Emden equations which form Volterra integro-differential equations.
The Lane-Emden equations are converted to Volterra integro-differential
equations and then are solved by the Legendre multi-wavelet method.
The properties of Legendre multi-wavelets are first presented.
The properties of Legendre multi-wavelets are used to reduce the system of
integral equations to a system of algebraic equations which can be solved
by any numerical method. Illustrative examples are discussed to show
the validity and applicability of the present method. |
| first_indexed | 2024-12-11T08:00:08Z |
| format | Article |
| id | doaj.art-fc51a5e92def403ab48b8b864eb9af8a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T08:00:08Z |
| publishDate | 2015-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-fc51a5e92def403ab48b8b864eb9af8a2022-12-22T01:15:08ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-01-01201528,111Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-waveletsPrakash Kumar Sahu0Santanu Saha Ray1 National Inst. of Technology Rourkela, India National Inst. of Technology Rourkela, India A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The properties of Legendre multi-wavelets are first presented. The properties of Legendre multi-wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved by any numerical method. Illustrative examples are discussed to show the validity and applicability of the present method.http://ejde.math.txstate.edu/Volumes/2015/28/abstr.htmlLegendre multi-waveletVolterra integral equationintegro-differential equationLane-Emden equation |
| spellingShingle | Prakash Kumar Sahu Santanu Saha Ray Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets Electronic Journal of Differential Equations Legendre multi-wavelet Volterra integral equation integro-differential equation Lane-Emden equation |
| title | Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets |
| title_full | Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets |
| title_fullStr | Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets |
| title_full_unstemmed | Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets |
| title_short | Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets |
| title_sort | numerical solutions for volterra integro differential forms of lane emden equations of first and second kind using legendre multi wavelets |
| topic | Legendre multi-wavelet Volterra integral equation integro-differential equation Lane-Emden equation |
| url | http://ejde.math.txstate.edu/Volumes/2015/28/abstr.html |
| work_keys_str_mv | AT prakashkumarsahu numericalsolutionsforvolterraintegrodifferentialformsoflaneemdenequationsoffirstandsecondkindusinglegendremultiwavelets AT santanusaharay numericalsolutionsforvolterraintegrodifferentialformsoflaneemdenequationsoffirstandsecondkindusinglegendremultiwavelets |