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.
Cite this paper
F. Alharbi, "Predefined Exponential Basis Set for Half-Bounded Multi Domain Spectral Method," Applied Mathematics, Vol. 1 No. 3, 2010, pp. 146-152. doi: 10.4236/am.2010.13019.
 P. Grandclement and J. Novak, “Spectral Methods for Numerical Relativity,” Living Reviews in Relativity, Vol. 12, No. 1, 2009, pp. 1-107.
J. Boyd, “Chebyshev and Fourier Spectral Methods,” Dover Publications, Mineola, 2001.
C. G. Canuto, M. Y. Hussaini, A. M. Quarteroni and T. A. Zang, “Spectral Methods: Fundamentals in Single Domains,” 1st Edition, Springer, New York, 2006.
A. Toselli and O. Widlund, “Domain Decomposition Methods,” Springer, Berlin, 2004.
D. Fructus, D. Clamond, J. Grue and ?. Kristiansen, “An Efficient Model for Three-Dimensional Surface Wave Simulations: Part I: Free Space Problems,” Journal of Computational Physics, Vol. 205, No. 2, 2005, pp. 665-685.
 B.-Y. Guo and J. Shen, “Irrational Approximations and their Applications to Partial Differential Equations in Exterior Domains,” Advances in Computational Mathematics, Vol. 28, No. 3, 2008, pp. 237-267.
B.-Y. Guo, “Jacobi Spectral Approximations to Differential Equations on the Half Line,” Journal of Computational Mathematics, Vol. 18, No. 1, 2000, pp. 95-112.
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.
V. Korostyshevskiy and T. Wanner, “A Hermite Spectral Method for the Computation of Homoclinic Orbits and Associated Functionals,” Journal of Computational and Applied Mathematics, Vol. 206, No. 2, 2007, pp. 986- 1006.
J. Shen and L.-L. Wang, “Some Recent Advances on Spectral Methods for Unbounded Domains,” Communications in Computational Physics, Vol. 5, No. 2-4, 2009, pp. 195-241.
C.-C. Huang, “Semiconductor Nanodevice Simulation by Multidomain Spectral Method with Chebyshev, Prolate Spheroidal and Laguerre Basis Functions,” Computer Physics Communications, Vol. 180, No. 1, 2009, pp. 375- 383.