Tjang Daniel, Chandra (2014) SOLVING A SYSTEM OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS BY USING DIAGONALIZATION MATRIX. Proceeding of International Conference On Research, Implementation And Education Of Mathematics And Sciences 2014. (Submitted)
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Abstract
Consider a system of fourth order ordinary differential equation x(4) = Ax, where A is a square matrix. To find the solution of this system, the matrix A will be diagonalized by using J =P-1AP, where P is a matrix with vectoreigens of A as its columns. Therefore, the original system can be transformed into a new system y(4) = Jy with y = P-1x. Solving this new system will yield the soluton of the original system, that is, x = Py. Some problems with different types of eigenvalues of A will be given. Especially, Jordan form is used to diagonalize A, when all eigenvalues of A are equal.
| Item Type: | Article |
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| Uncontrolled Keywords: | fourth order ordinary differential equation, diagonalization matrix |
| Subjects: | Prosiding > ICRIEMS 2014 > MATHEMATICS & MATHEMATICS EDUCATION |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Pendidikan Matematika > Matematika |
| Depositing User: | Eprints |
| Date Deposited: | 07 Nov 2014 04:28 |
| Last Modified: | 07 Nov 2014 04:28 |
| URI: | http://eprints.uny.ac.id/id/eprint/11510 |
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