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J. Valenciano and M. Chaplain, “A Laguerre-Legendre Spectral-Element Method for the Solution of Partial Differential Equations on Infinite Domains: Application to the Diffusion of Tumour Angiogenesis Factors,” Mathematical and Computer Modelling, Vol. 41, No. 2-3, 2005, pp. 1171-1192.

has been cited by the following article:

• TITLE: Predefined Exponential Basis Set for Half-Bounded Multi Domain Spectral Method

  AUTHORS: Fahhad Alharbi

  KEYWORDS: Multi-Domain Spectral Method, Meshfree Numerical Method, Non-Orthogonal Predefined, Exponential Basis Set, Half-Bounded Domain, Exponential Decay, Quantum Wells, Optical Waveguide

  JOURNAL NAME: Applied Mathematics, Vol.1 No.3, September 29, 2010

  ABSTRACT: A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.