The method of fundamental solutions for linear diffusion-reaction equations

Mathematical and Computer Modelling

Volumn 31, Issue 2-3, 2000, Pages 221-237

  Balakrishnan, K ^a   Ramachandran, P A ^a  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Geometric singularities; Linear diffusion reaction equations; Method of fundamental solutions; Multiply connected domains; Orthogonal collocation

Indexed keywords

EID: 0033996710     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(99)00233-2     Document Type: Article

References (24)

1. P.W. Partridge, C.A. Brebbia and L.C. Wrobel, The Dual Reciprocity Boundary Element Method, Computational Mechanics Publications, (1992).
2. P.A. Ramachandran, Boundary Element Methods in Transport Phenomena, Computational Mechanics Publications, Boston, MA, (1993).
3. K.E. Atkinson and D. Chien, Piecewise polynomial collocation for boundary integral equations, SIAM Journal on Scientific and Statistical Computing 76, 651-681, (1998).
4. M.A. Golberg and C.S. Chen, Discrete Projection Methods for Integral Equations, Computational Mechanics Publications, Southampton, (1996).
5. A. Karageorghis and G. Fairweather, The simple layer potential method of fundamental solutions for certain biharmonic problems, International Journal for Numerical Methods in Fluids 9 (10), 1221-1234, (1989).
6. A. Karageorghis and G. Fairweather, The method of fundamental solutions for the solution of non-linear plane potential problems, IMA Journal of Numerical Analysis 9, 231-242, (1989).
7. A. Karageorghis and G. Fairweather, The method of fundamental solutions for the numerical solution of the biharmonic equation, Journal of Computational Physics 69, 435-459, (1987).
8. A. Karageorghis, Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities, Numerical Methods for Partial Differential Equations 8, 145-161, (1990).
9. A. Poullikkas, A. Karageorghis and G. Georgiou, The method of fundamental solutions for harmonic and biharmonic boundary value problems, Computational Mechanics (to appear).
10. M. Katsurada, Charge simulation method using exterior mapping functions, Japan Journal of Industrial and Applied Mathematics 11, 47-61, (1994).
11. R.L. Johnston and G. Fairweather, The method of fundamental solutions for problems in potential flow, Applied Mathematical Modeling 8, 265-270, (1989).
12. M. Katsurada and H. Okamota, The collocation points of the fundamental solution method for the potential problem, Computers Math. Applic. 31 (1), 123-137, (1996).
13. T. Kitagawa, Asymptotic stability of the fundamental solution method, Journal of Computational and Applied Mathematics 38, 263-269, (1991).
14. A.A. Rogovoy, The source method in elasticity theory, International Journal of Boundary Element Communications 8, 141-149, (1997).
15. C.S. Chen, Y.F. Rashed and M.A. Golberg, A mesh free method for linear diffusion equations, Numerical Heat Transfer (to appear).
16. S.R. Karur and P.A. Ramachandran, Orthogonal collocation in the boundary element method, Journal of Computational Physics 121 (2), 373-382, (1995).
17. J. Villadsen and S. Michelsen, Solution to Differential Equation Modeling by Polynomial Approximation, Prentice-Hall, New York, (1978).
18. A.P. Zielinski and I. Herrera, Trefftz method: Fitting boundary conditions, International Journal for Numerical Methods in Engineering 24 (5), 871-891, (1987).
19. R.S.C. Cheng, Delta Trigonometric and Spline Methods Using the Single-layer Potential Representation, Ph.D. Thesis, University of Maryland, (1987).
20. R. Bialecki, R. Daliner and G. Kunn, New application of hypersingular equations in the boundary element method, Computer Methods in Applied Mechanics and Engineering 103 (3), 399-416, (1988).
21. P.L. Mills, S. Lai, M.P. Dudukovic and P.A. Ramachandran, Numerical study of approximation methods for solution of linear and nonlinear diffusion-reaction equations with discontinuous boundary conditions, Computers and Chemical Engineering 12 (1), 37-53, (1988).
22. S. Christiansen and P.C. Hansen, The effective condition number applied to error analysis of certain boundary collocation methods, Journal of Computational and Applied Mathematics 54, 15-36, (1994).
23. S.R. Karur and P.A. Ramachandran, Solving linear diffusion-reaction networks is porous catalyst particles using BEM, AIChE Journal 42 (2), 383-390, (1997).
24. L.C. Nitsche and H. Brenner, Hydrodynamics of particulate motion in sinusoidal pores via a singularity method, AIChE Journal 36 (9), 1403-1419, (1990).