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Cited by 22 publications
(19 citation statements)
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“…The results are provided in Table 10 at S * = (100, 100, 100) T using the reference solution 26.213 provided by a very refined grid [1]. Note also that we considered λ = 1000 and ∆τ = 2.5 × 10 −3 while the computational domains for the Yousuf et al method [26] As can be seen from the results, the RBF Wendland scheme using the modified Hardy algorithm converge to the reference solution while the finite difference technique of [26] requires more number of nodes. The results of comparisons in this case are given in Table 11 and we used (3.5) for constructing the constant shape parameter to the reference solution 13.659.…”
Section: Computational Experimentsmentioning
confidence: 99%
“…The results are provided in Table 10 at S * = (100, 100, 100) T using the reference solution 26.213 provided by a very refined grid [1]. Note also that we considered λ = 1000 and ∆τ = 2.5 × 10 −3 while the computational domains for the Yousuf et al method [26] As can be seen from the results, the RBF Wendland scheme using the modified Hardy algorithm converge to the reference solution while the finite difference technique of [26] requires more number of nodes. The results of comparisons in this case are given in Table 11 and we used (3.5) for constructing the constant shape parameter to the reference solution 13.659.…”
Section: Computational Experimentsmentioning
confidence: 99%
“…Using Duhamel's principle, an approach similar to Kleefeld et al and Yousuf et al , we can show that u normalα ( t n ) , 1 α m o , 0 < n N satisfy the following recurrent formula: u normalα ( t n + 1 ) = e k A normalα u normalα ( t n ) + 0 k e A α false( k normalτ false) F normalα ( u 1 ( t n + τ ) , u 2 ( t n + τ ) , , u m o ( t n + τ ) , t n + τ ) d τ The integral in (2.6) can be approximated by a class of exponential time differencing (ETD) numerical schemes, see for example and references therein. Denoting the approximation to u normalα ( t n ) by u α , n and the approximation to a normalα ( t n ) by a α , n , the second order exponential time differencing Runge–Kutta semidiscrete scheme is given by , u α , …”
Section: Partial Integral Differential Equationsmentioning
confidence: 99%
“…Let 0 < k ≤ k 0 , for some k 0 , be the fixed time step and t n = nk, 0 ≤ n ≤ N, k = Δt. Using Duhamel's principle, an approach similar to Kleefeld et al [23] and Yousuf et al [1,3], we can show that u α (t n ), 1 ≤ α ≤ m o , 0 < n ≤ N satisfy the following recurrent formula:…”
Section: )mentioning
confidence: 99%
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