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  • 1
    Electronic Resource
    Electronic Resource
    The method of fundamental solutions for non-linear thermal explosions (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 675-681 
    Details
    ISSN: 1069-8299
    Keywords: blow-up ; method of fundamental solutions ; BEM ; thin plate spline ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method based on the method of fundamental solutions, thin plate spine interpolation and monotone iteration is devised to find the minimal solution of the steady-state blow-up problem. The method of fundamental solutions requires neither domain nor boundary discretization and results in high accuracy and efficiency. For illustration, critical values of the Frank-Kamenetskii parameter are given for different geometrical boundaries in the two-dimensional case.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110806
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1421-1435 
    Details
    ISSN: 0029-5981
    Keywords: method of fundamental solutions ; particular solution ; diffusion equations ; quasi-Monte-Carlo method ; Laplace transform ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Laplace transform is applied to remove the time-dependent variable in the diffusion equation. For non-harmonic initial conditions this gives rise to a non-homogeneous modified Helmholtz equation which we solve by the method of fundamental solutions. To do this a particular solution must be obtained which we find through a method suggested by Atkinson. To avoid costly Gaussian quadratures, we approximate the particular solution using quasi-Monte-Carlo integration which has the advantage of ignoring the singularity in the integrand. The approximate transformed solution is then inverted numerically using Stehfest's algorithm. Two numerical examples are given to illustrate the simplicity and effectiveness of our approach to solving diffusion equations in 2-D and 3-D. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    A numerical method for heat transfer problems using collocation and radial basis functions (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 1263-1278 
    Details
    ISSN: 0029-5981
    Keywords: heat transfer ; collocation ; radial basis functions ; random points ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Simple, mesh/grid free, numerical schemes for the solution of heat transfer problems are developed and validated. Unlike the mesh or grid-based methods, these schemes use well-distributed quasi-random collocation points and approximate the solution using radial basis functions. The schemes work in a similar fashion as finite differences but with random points instead of a regular grid system. This allows the computation of problems with complex-shaped boundaries in higher dimensions with no extra difficulty. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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