Analytical Solutions of Generalised Emden–Fowler Initial and Boundary Value Problems of Higher Order
In this paper, the analytical solutions of a class of generalised linear and nonlinear Emden–Fowler-type equations of higher order are presented using a power series method. The proposed equations are subject to appropriate initial and boundary conditions. A generalised Cauchy product is applied to...
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| Published in | International journal of applied and computational mathematics Vol. 10; no. 2 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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01.04.2024
Springer Nature B.V |
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| Abstract | In this paper, the analytical solutions of a class of generalised linear and nonlinear Emden–Fowler-type equations of higher order are presented using a power series method. The proposed equations are subject to appropriate initial and boundary conditions. A generalised Cauchy product is applied to reduce the nonlinear terms to power series whose expansion coefficients are expressed recursively as finite sums involving the expansion coefficients of the assumed series solution. In the case of boundary value problems, required initial conditions are assumed and introduced as dummy constants, which are subsequently determined using the corresponding right boundary conditions. Several examples of Emden–Fowler-type initial and boundary value problems of the third, fourth, fifth, and sixth orders are explicitly given to illustrate the proposed method. For comparison purposes, we consider known problems in the literature. Interestingly, in all the examples considered, our series solutions agree excellently with the exact solutions and published results in the literature. |
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| AbstractList | In this paper, the analytical solutions of a class of generalised linear and nonlinear Emden–Fowler-type equations of higher order are presented using a power series method. The proposed equations are subject to appropriate initial and boundary conditions. A generalised Cauchy product is applied to reduce the nonlinear terms to power series whose expansion coefficients are expressed recursively as finite sums involving the expansion coefficients of the assumed series solution. In the case of boundary value problems, required initial conditions are assumed and introduced as dummy constants, which are subsequently determined using the corresponding right boundary conditions. Several examples of Emden–Fowler-type initial and boundary value problems of the third, fourth, fifth, and sixth orders are explicitly given to illustrate the proposed method. For comparison purposes, we consider known problems in the literature. Interestingly, in all the examples considered, our series solutions agree excellently with the exact solutions and published results in the literature. |
| ArticleNumber | 43 |
| Author | Awonusika, Richard Olu |
| Author_xml | – sequence: 1 givenname: Richard Olu surname: Awonusika fullname: Awonusika, Richard Olu email: richard.awonusika@aaua.edu.ng organization: Department of Mathematical Sciences, Adekunle Ajasin University |
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| Keywords | 35A08 65L05 Power series method 34B16 33C45 Emden–Fowler equation Generalised Emden–Fowler-type equation Generalised Cauchy product 33C05 Series solution 34A08 |
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| Snippet | In this paper, the analytical solutions of a class of generalised linear and nonlinear Emden–Fowler-type equations of higher order are presented using a power... |
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| SubjectTerms | Applications of Mathematics Boundary conditions Boundary value problems Computational Science and Engineering Exact solutions Initial conditions Mathematical analysis Mathematical and Computational Physics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Nuclear Energy Operations Research/Decision Theory Original Paper Power series Theoretical Thermal expansion |
| Title | Analytical Solutions of Generalised Emden–Fowler Initial and Boundary Value Problems of Higher Order |
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