The method of fundamental solutions for non‐linear thermal explosions
- 1 August 1995
- journal article
- research article
- Published by Wiley in Communications in Numerical Methods in Engineering
- Vol. 11 (8) , 675-681
- https://doi.org/10.1002/cnm.1640110806
Abstract
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.Keywords
This publication has 10 references indexed in Scilit:
- On a method of Atkinson for evaluating domain integrals in the boundary element methodApplied Mathematics and Computation, 1994
- The Theory of Radial Basis Function Approximation in 1990Published by Oxford University Press (OUP) ,1992
- The multiple-reciprocity method. A new approach for transforming BEM domain integrals to the boundaryEngineering Analysis with Boundary Elements, 1989
- A numerical method for semilinear singular parabolic quenching problemsQuarterly of Applied Mathematics, 1989
- Fundamental Solutions Method for Elliptic Boundary Value ProblemsSIAM Journal on Numerical Analysis, 1985
- Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous ReactionsSIAM Journal on Applied Mathematics, 1983
- Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach SpacesSIAM Review, 1976
- Spontaneous Ignition: Finite Element Solutions for Steady and Transient ConditionsJournal of Heat Transfer, 1974
- Thermal theory of spontaneous ignition: criticality in bodies of arbitrary shapePhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1971
- Thermal Initiation of ExplosivesJournal of Applied Physics, 1960