An Improved Method of Un determined Coefficients
- Lesław Kwaśniewski
An exact solution method in terms of an infinite power series is developed for linear ordinary differential equations with polynomial coefficients. The method is general and applicable to a wide range of equations of any N-th order presented in normal form. The final solution is defined by a linear combination of S functions fj(x) j=1,...,S expressed in the form of a power series, and by additional (S-N) number of accompanied relationships for unknown constants. Each term of the series fj(x) is defined by a finite number of operations involving matrix calculations. The term calculation is independent on unknown constants. The method is also applicable to any system of R differential equations in normal form with the restriction that all equations in the system are of the same order. The advantage over the "classical" method of undetermined coefficients is that here the recursions are of first order even for higher-order differential equations. The general solution is expressed explicitly in the form allowing for application of any form of initial, boundary, or combined conditions. The paper presents the development of the method and, as examples, its application to solving selected second- and third-order differential equations.
- Record ID
- Journal series
- The Open Applied Mathematics Journal, ISSN 1874-1142
- Issue year
- DOI:10.2174/1874114200903010033 Opening in a new tab
- http://www.benthamscience.com/open/toamj/openaccess2.htm Opening in a new tab
- (en) English
- File: 1
- Score (nominal)
- Score source
- Uniform Resource Identifier
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.