Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method
We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2692 |
| _version_ | 1797512093040115712 |
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| author | Bogdan Căruntu Mădălina Sofia Paşca |
| author_facet | Bogdan Căruntu Mădălina Sofia Paşca |
| author_sort | Bogdan Căruntu |
| collection | DOAJ |
| description | We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a fact that is illustrated by the numerical examples presented. The comparison with previous approximations computed for the included test problems emphasizes the method’s simplicity and accuracy. |
| first_indexed | 2024-03-10T05:57:02Z |
| format | Article |
| id | doaj.art-99765c6f1be5456e804227fa0939b9d8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:57:02Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-99765c6f1be5456e804227fa0939b9d82023-11-22T21:17:27ZengMDPI AGMathematics2227-73902021-10-01921269210.3390/math9212692Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares MethodBogdan Căruntu0Mădălina Sofia Paşca1Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, RomaniaDepartment of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, RomaniaWe apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a fact that is illustrated by the numerical examples presented. The comparison with previous approximations computed for the included test problems emphasizes the method’s simplicity and accuracy.https://www.mdpi.com/2227-7390/9/21/2692Volterra and Fredholm nonlinear integro-differential equationsapproximate analytic polynomial solutionpolynomial least squares method |
| spellingShingle | Bogdan Căruntu Mădălina Sofia Paşca Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method Mathematics Volterra and Fredholm nonlinear integro-differential equations approximate analytic polynomial solution polynomial least squares method |
| title | Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method |
| title_full | Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method |
| title_fullStr | Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method |
| title_full_unstemmed | Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method |
| title_short | Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method |
| title_sort | approximate solutions for a class of nonlinear fredholm and volterra integro differential equations using the polynomial least squares method |
| topic | Volterra and Fredholm nonlinear integro-differential equations approximate analytic polynomial solution polynomial least squares method |
| url | https://www.mdpi.com/2227-7390/9/21/2692 |
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