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Hyers–Ulam Stability of Order k for Euler Equation and Euler–Poisson Equation in the Calculus of Variations

2022
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Mathematics
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In this paper, we define and study Hyers–Ulam stability of order 1 for Euler's equation and Hyers–Ulam stability of order m−1 for the Euler–Poisson equation in the calculus of variations in two special cases, when these equations have the form y″(x)=f(x) and y(m)(x)=f(x), respectively. We prove some estimations for Jyx−Jy0x, where y is an approximate solution and y0 is an exact solution of the corresponding Euler and Euler-Poisson equations, respectively. We also give two examples.

doi:10.3390/math10152556
fatcat:siljeyk7dje6njsznzex7d4yjy