Main Article Content

Abstract

This paper discusses Green’s matrix of nonlinear boundary value problem of first-order differential system with rectangular coeffisients, especially about its properties. In this case, the differential equation of the form  with boundary conditions of the form   and  which  is a real  matrix with  whose entries are continuous on  and . ,  are nonsingular matrices such that  and  are constant vectors. To get the Green’s matrix and the assosiated generalized Green’s matrix, we change the boundary condition problem into an equivalent  differential equation by using the properties of the  Moore-Penrose generalized inverse, then  its solution is found by using method of variation of parameters. The last we prove  that the defined matrices  satisfy the properties of green’s function. The result is the corresponding the Green’s matrix and the assosiated generalized Green’s matrix have the property of Green’s functions with the jump-discontinuity.

Keywords

Green’s matrix nonlinear first-order differential

Article Details

How to Cite
1.
Badrulfalah B, Susanti D, Joebaedi K, Kosasih R. Some Properties of Green’s Matrix of Nonlinear Boundary Value Problem of First Order Differential. Eksakta [Internet]. 2019Apr.28 [cited 2020Jul.8];20(1):41-7. Available from: http://eksakta.ppj.unp.ac.id/index.php/eksakta/article/view/173

References

  1. A. S. Delf. 1982. Advanced Matrix Theory for Scientists and Engineers. Abacus Press. London.
  2. Badrulfalah. 1992. Masalah Syarat Batas Dua Titik. Thesis Program S2 Matematika ITB. Tidak Dipublikasikan. Bandung. ITB.
  3. Boyce, E., William and Diprima, C., Richard.1992. Elementary Differential Equations and Boundary Value Problem (5nd Edition). Canada: John Willey & Sons. Inc.
  4. Braun, Martin. 1982. Differential Equqtions and their Applications (3nd Edition). New York. Heidelberg Berlin: Springer-Verlag
  5. Cole, R. H. 1968. Theory of Ordinary Differential Equations. Appleton-Century-Croft, New York.
  6. Deo, S. G. , V. Raghavendra. 1987. Ordinary Differential Equations And Stability Theory. Tata McGraw-Hill Publ. Co. Ltd., New Delhi.
  7. Murti, K. N., P. V. S. Lakshmi. 1990. On Two- Point Boundary Value Problems. Journal of Mathematical analysis And Applications 153, 217-225.
  8. P. Lancaster and M. Tismenetsky. 1985. The Theory of Matrices. Academic Press. New York
  9. Uvah J. A. & Vatsala A. S. 1990. Monotone Iterative Technique for Nonlinear Boundary-Value Problem of First Order Differential System with Rectangulatr Coeffisients. Journal of Mathematical analysis and Applications, 482-49.

Most read articles by the same author(s)