A new perturbative technique for solving integro-partial differential equations

Journal of Mathematical Physics

Volumn 40, Issue 10, 1999, Pages 5224-5239

  Becker, Peter A ^a  

^a GEORGE MASON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033240859     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533026     Document Type: Article

References (17)

1. J. Satsuma and M. Mimura, "Stability properties of spatially periodic solutions for nonlinear diffusion equations with a singular integral term," Jpn. J. Appl. Math. 4, 59-72 (1987).
2. E. Sonnendrücker, J. Roche, P. Bertrand, and A. Ghizzo, "The semi-Lagrangian method for the numerical resolution of the Vlasov equation," J. Comput. Phys. 149, 201-220 (1999).
3. P. Knabner and L. von Wolfersdorf, "Travelling wave solutions of a system of nonlinear diffusion equations with integral term," Z. Anal. Anwendungen 10, 503-512 (1991).
4. D. Wang, "Global solutions and stability for self-gravitating isentropic gases," J. Math. Anal. Appl. 229, 530-542 (1999).
5. P. A. Becker and M. C. Begelman, "Comptonization in supercritical winds. I. Spectral evolution," Astrophys. J. 310, 534-551 (1986).
6. G. B. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics (Wiley, New York, 1979).
7. R. M. Thomas and T. E. Simos, "A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation," J. Comput. Appl. Math. 87, 215-226 (1997).
8. P. K. Lamm, "Approximation of ill-posed Volterra problems via predictor-corrector regularisation methods," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 56, 524-541 (1996).
9. V. J. Ervin and W. J. Layton, "A robust and parallel relaxation method based on algebraic splittings," Numer. Methods Partial Differential Equations 15, 91-110 (1999).
10. F. Liu, "Convergence of approximate solutions for quasilinear hyperbolic conservation laws with relaxation," J. Partial Differential Eqs. 11, 289-300 (1998).
11. H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer, Berlin, 1989).
12. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
13. G. A. Baker and P. R. Graves-Morris, Encyclopedia of Mathematics and its Applications (Addison-Wesley, Reading, MA, 1981), Vols. 13 and 14.
14. A. S. Kompaneets, "The establishment of thermal equilibrium between quanta and electrons," Sov. Phys. JETP 4, 730-737 (1957).
15. P. A. Becker, "A self-consistent theory of photohydrodynamical shocks," Astrophys. J. 327, 772-793 (1988).
16. G. Jumarie, "Solution of the multivariate Fokker-Planck equation by using a maximum paih entropy principle," J. Math. Phys. 31, 2389-2392 (1990).
17. C. Bender, S. Boettcher, and K. A. Milton, "A new perturbative approach to nonlinear partial differential equations," J. Math. Phys. 32, 3031-3038 (1991).