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(7 citation statements)

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“…Similar results hold for the piecewise interpolation error y−ψ N (y) in the norms of the Sobolev spaces (see Theorem 1 of [40]). In the next theorem, we shall give an estimate in the maximum norm.…”

confidence: 64%

“…Similar results hold for the piecewise interpolation error y−ψ N (y) in the norms of the Sobolev spaces (see Theorem 1 of [40]). In the next theorem, we shall give an estimate in the maximum norm.…”

confidence: 64%

“…On the other hand, in global pseudospectral methods it is not convenient to resolve the corresponding discrete system with very large number of collocation points. To remove this deficiency, adaptive version of pseudospectral method, which is based on the domain decomposition procedure, is considered [38][39][40]. To the best of our knowledge, adaptive pseudospectral methods are not well studied for solving fractional differential equations.…”

confidence: 99%

“…The results obtained via Lagrange polynomials [4], Triangular function [11] and adaptive Legendre-Gauss-Radau collocation method [17] are to that shown in Table 1. We mention in [17], N is the number of subintervals of the adaptive collocation method. Here, the solution of this example is obtained by choosing N = 7.…”

confidence: 92%

“…We now review some error bounds for the above approximations. According to Reference 25 formula (5.4.33), whenever u ∈ H s ( I ) , the Sobolev space of integer order $s\u2a7e1$, one has (consult 27 ), $${\Vert u-{\mathcal{I}}^{N}u\Vert}_{{L}^{2}(I)}^{2}\u2a7dC{N}^{-2s}{\displaystyle \sum _{l=\mathrm{min}false\{s,N+1false\}}^{s}}{h}^{2l}{\Vert {u}^{(l)}\Vert}_{{L}^{2}(I)}^{2},$$ where u ( l ) is the distributional derivative of function u of order l . In addition, C denotes a positive constant that depends on s , but which is independent of the function u and integer N .…”

confidence: 99%