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Maleki, Mohammad; Hashim, Ishak; Abbasbandy, Saeid

Analysis of IVPs and BVPs on semi-infinite domains via collocation methods. (English) Zbl 1244.76067

J. Appl. Math. 2012, Article ID 696574, 21 p. (2012).
Summary: We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformation is used to map the semi-infinite domain \(x \in [0, \infty)\) onto a half-open interval \(t \in [-1, 1)\). The resulting finite-domain two-point boundary value problem is transcribed to a system of algebraic equations using Chebyshev-Gauss (CG) collocation, while the resulting initial value problem over a finite domain is transcribed to a system of algebraic equations using Chebyshev-Gauss-Radau (CGR) collocation. In numerical experiments, the tuning of the map \(\phi : [-1, +1) \rightarrow [0, +\infty)\) and its effects on the quality of the discrete approximation are analyzed.

Cited in 5 Documents

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76S05 Flows in porous media; filtration; seepage
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\textit{M. Maleki} et al., J. Appl. Math. 2012, Article ID 696574, 21 p. (2012; Zbl 1244.76067)
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