Skip to main content
placeholder image

On a generalisation of the fundamental matrix and the solution of operator equations

Journal Article


Abstract


  • We consider a broad class of linear operator equations that includes systems of ordinary differential equations, difference equations and fractional-order ordinary differential equations. This class also includes operator exponentials and powers, as well as eigenvalue problems and Fredholm integral equations. Many problems in engineering and the physical and natural sciences can be described by such operator equations. We generalise the fundamental matrix to a fundamental operator and provide a new explicit method for obtaining an exact series solution to these types of operator equations, together with sufficient conditions for convergence and error bounds. Illustrative examples are also given.

Publication Date


  • 2020

Citation


  • Rodrigo, M. R. (2020). On a generalisation of the fundamental matrix and the solution of operator equations. International Journal of Applied Mathematics, 33 (3), 413-438.

Scopus Eid


  • 2-s2.0-85087978571

Number Of Pages


  • 25

Start Page


  • 413

End Page


  • 438

Volume


  • 33

Issue


  • 3

Place Of Publication


  • Bulgaria

Abstract


  • We consider a broad class of linear operator equations that includes systems of ordinary differential equations, difference equations and fractional-order ordinary differential equations. This class also includes operator exponentials and powers, as well as eigenvalue problems and Fredholm integral equations. Many problems in engineering and the physical and natural sciences can be described by such operator equations. We generalise the fundamental matrix to a fundamental operator and provide a new explicit method for obtaining an exact series solution to these types of operator equations, together with sufficient conditions for convergence and error bounds. Illustrative examples are also given.

Publication Date


  • 2020

Citation


  • Rodrigo, M. R. (2020). On a generalisation of the fundamental matrix and the solution of operator equations. International Journal of Applied Mathematics, 33 (3), 413-438.

Scopus Eid


  • 2-s2.0-85087978571

Number Of Pages


  • 25

Start Page


  • 413

End Page


  • 438

Volume


  • 33

Issue


  • 3

Place Of Publication


  • Bulgaria