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- Title
On Explicit Formulas of Hyperbolic Matrix Functions.
- Authors
Laarichi, Y.; Elkettani, Y.; Gretete, D.; Barmaki, M.
- Abstract
Hyperbolic matrix functions are essential for solving hyperbolic coupled partial differential equations. In fact the best analytic-numerical approximations for resolving these equations come from the use of hyperbolic matrix functions. The hyperbolic matrix sine and cosine sh(A), ch(A) (A ∈ Mr(C)) can be calculated using numerous different techniques. In this article we derive some explicit formulas of sh(tA) and ch(tA) (t ∈ R) using the Fibonacci-Hörner and the polynomial decomposition, these decompositions are calculated using the generalized Fibonacci sequences combinatorial properties in the algebra of square matrices. Finally we introduce a third approach based on the homogeneous linear differential equations. And we provide some examples to illustrate your methods.
- Subjects
HYPERBOLIC functions; MATRIX functions; LINEAR differential equations; FIBONACCI sequence; PARTIAL differential equations
- Publication
Malaysian Journal of Mathematical Sciences, 2023, Vol 17, Issue 2, p201
- ISSN
1823-8343
- Publication type
Article
- DOI
10.47836/mjms.17.2.08