Sinc approximation of the heat distribution on the boundary of a two-dimensional finite slab

Abstract

We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation function is represented by a two-dimensional Sinc series and the error estimate is given. ᭧

Corrigendum to a fractional sideways problem in a one‐dimensional finite‐slab with deterministic and random interior perturbed data

“…is continuous with respect to h 𝑓 t ∈ L 2 (R). In this case, we can put (18) and consider the problem of regularizing the function u such that…”

“…However, in practice, it is difficult to accurately measure the interior heat flux. Hence, a more feasible way is finding the function u(x, t) from measurements u(x 1 , t), … , u(x k , t) at many interior points x 1 , … , x k of the body (see, e.g., Dinh et al [18]). MingLia and Xiong [19] and Tautenhahn [20] used an interior measurement u(x 0 , t) and an assumption at infinity lim x→∞ u(x, t) = 0 to recover u(x, t).…”

“…However, in practice, it is difficult to accurately measure the interior heat flux. Hence, a more feasible way is finding the function $$$ u\left(x,t\right) $$$ from measurements $$$ u\left({x}_1,t\right),\dots, u\left({x}_k,t\right) $$$ at many interior points $$$ {x}_1,\dots, {x}_k $$$ of the body (see, e.g., Dinh et al [18]). MingLia and Xiong [19] and Tautenhahn [20] used an interior measurement $$$ u\left({x}_0,t\right) $$$ and an assumption at infinity $$$ {\lim}_{x\to \infty }u\left(x,t\right)=0 $$$ to recover $$$ u\left(x,t\right) $$$.…”

Sinc Collocation Method for Finding Numerical Solution of Integrodifferential Model Arisen in Continuous Mixed Strategy

“…In the last three decades a variety of numerical methods based on the sinc approximation have been developed. Sinc methods were developed by Stenger [15] and Lund and Bowers [16] and it is widely used for solving a wide range of linear and nonlinear problems arising from scientific and engineering applications including oceanographic problems with boundary layers [17], two-point boundary value problems [18], astrophysics equations [19], Blasius equation [20], Volterras population model [21], Hallens integral equation [22], third-order boundary value problems [23], system of second-order boundary value problems [24], fourth-order boundary value problems [25], heat distribution [26], elastoplastic problem [27], inverse problem [28,29], integrodifferential equation [30], optimal control [15], nonlinear boundary-value problems [31], and multipoint boundary value problems [32]. Very recently authors of [33] used the sinc procedure to solve linear and nonlinear Volterra integral and integrodifferential equations.…”

A fractional sideways problem in a one‐dimensional finite‐slab with deterministic and random interior perturbed data

“…However, in practice, it is difficult to accurately measure the interior heat flux. Hence, a more feasible way is finding the function u(x, t) from measurements u(x 1 , t), … , u(x k , t) at many interior points x 1 , … , x k of the body (see, eg, Dinh et al 18 ). Li et al 19 and Tautenhahn 20 used an interior measurement u(x 0 , t) and an assumption at infinity lim x→∞ u(x, t) = 0 to recover u(x, t).…”