The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

76 Scopus Citations
View graph of relations


Related Research Unit(s)


Original languageEnglish
Pages (from-to)1421-1435
Journal / PublicationInternational Journal for Numerical Methods in Engineering
Issue number8
Publication statusPublished - 30 Dec 1998


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.

Research Area(s)

  • Diffusion equations, Laplace transform, Method of fundamental solutions, Particular solution, Quasi-Monte-Carlo method

Citation Format(s)