We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Ulam–Hyers Stability of Second-Order Convergent Finite Difference Scheme for First- and Second-Order Nonhomogeneous Linear Differential Equations with Constant Coefficients.
- Authors
Bora, Swaroop Nandan; Shankar, Matap
- Abstract
This article studies the Ulam–Hyers stability of the second-order convergent finite difference scheme for the first- and second-order non-homogeneous linear differential equations x ′ (t) - b x (t) = f (t) and x ′ ′ (t) + α x ′ (t) + β x (t) = g (t) , on the interval I = [ a , ∞) , respectively, where f , g : I → R are given functions and a , b , α , β ∈ R. After converting the finite difference scheme to its equivalent linear recurrence relation and by using the Ulam–Hyers stability results for the linear recurrence relation, we establish the Ulam–Hyers stability for the finite difference scheme. Further, as per the location of the roots of the characteristic polynomial of the equivalent recurrence relation, the minimum Ulam–Hyers constant is determined. To illustrate the utility of the obtained result, we apply our result to the perturbed second-order nonlinear difference equation and present a suitable example at the end to support the obtained result.
- Subjects
ULAM, Stanislaw M., 1909-1984; FINITE differences; COMPUTATIONAL fluid dynamics; DIFFERENTIAL equations; LINEAR differential equations
- Publication
Results in Mathematics / Resultate der Mathematik, 2023, Vol 78, Issue 1, p1
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-022-01791-5