East Asian J. Appl. Math., 10 (2020), pp. 838-850.
Published online: 2020-08
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Let $\{ƒ_n\}^∞_{n=1}$ be a basis for $L_2([0, 1])$ and $\{g_n\}^∞_{n=1}$ be a system of functions of controlled decay on [0,∞). Considering a function u(x, t) that can be the represented in the form
where an ∈ R, x ∈ [0, 1] and t ∈ [0,∞), we investigate whether the function ƒ(x) =
u(x, 0) can be approximated, in a reasonable sense, by using data u(x0, t1), u(x0, t2),...,
u(x0, tN). A mathematical framework and efficient computational schemes are developed to determine approximate solutions for various classes of partial differential equations via sampled data by first establishing a near-best approximation of ƒ .
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Let $\{ƒ_n\}^∞_{n=1}$ be a basis for $L_2([0, 1])$ and $\{g_n\}^∞_{n=1}$ be a system of functions of controlled decay on [0,∞). Considering a function u(x, t) that can be the represented in the form
where an ∈ R, x ∈ [0, 1] and t ∈ [0,∞), we investigate whether the function ƒ(x) =
u(x, 0) can be approximated, in a reasonable sense, by using data u(x0, t1), u(x0, t2),...,
u(x0, tN). A mathematical framework and efficient computational schemes are developed to determine approximate solutions for various classes of partial differential equations via sampled data by first establishing a near-best approximation of ƒ .
Let $\{ƒ_n\}^∞_{n=1}$ be a basis for $L_2([0, 1])$ and $\{g_n\}^∞_{n=1}$ be a system of functions of controlled decay on [0,∞). Considering a function u(x, t) that can be the represented in the form
where an ∈ R, x ∈ [0, 1] and t ∈ [0,∞), we investigate whether the function ƒ(x) =
u(x, 0) can be approximated, in a reasonable sense, by using data u(x0, t1), u(x0, t2),...,
u(x0, tN). A mathematical framework and efficient computational schemes are developed to determine approximate solutions for various classes of partial differential equations via sampled data by first establishing a near-best approximation of ƒ .