Abstract
In this paper, we investigate the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of the homogeneous linear differential equation of nth order with initial and boundary conditions by using Taylor’s Series formula.
Highlights
The study of stability problem for various functional equations originated from a famous talk of S
In 1940, Ulam [1] posed a problem concerning the stability of functional equations: “Give Conditions in order for a linear function near an approximately linear function to exist.”
We prove the Hyers-Ulam-Rassias stability of the linear differential equation (1.1) with boundary conditions (1.3)
Summary
The study of stability problem for various functional equations originated from a famous talk of S. In 1940, Ulam [1] posed a problem concerning the stability of functional equations: “Give Conditions in order for a linear function near an approximately linear function to exist.”. Since this question has attracted the attention of many researchers. Note that first solution to this question was given by Hyers [2] in 1941 He made a significant breakthrough, when he gave an affirmative answer to the Ulam’s problem for additive functions defined on Banach Spaces. Numerical Analysis, Optimization, Biology, and Economics etc., where finding the exact solution is quite difficult It helps if the stochastic effects are small, to use deterministic model to approximate a stochastic one.
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