Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators
We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of genera...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/454865 |
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| author | K. Zhukovsky |
| author_facet | K. Zhukovsky |
| author_sort | K. Zhukovsky |
| collection | DOAJ |
| description | We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated. |
| format | Article |
| id | doaj-art-8d6d3708581341e195ef1922abd09358 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-8d6d3708581341e195ef1922abd093582025-02-03T01:02:17ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/454865454865Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential OperatorsK. Zhukovsky0Faculty of Physics, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119899, RussiaWe present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.http://dx.doi.org/10.1155/2014/454865 |
| spellingShingle | K. Zhukovsky Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators The Scientific World Journal |
| title | Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators |
| title_full | Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators |
| title_fullStr | Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators |
| title_full_unstemmed | Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators |
| title_short | Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators |
| title_sort | solution of some types of differential equations operational calculus and inverse differential operators |
| url | http://dx.doi.org/10.1155/2014/454865 |
| work_keys_str_mv | AT kzhukovsky solutionofsometypesofdifferentialequationsoperationalcalculusandinversedifferentialoperators |