Optimal and near-optimal advection-diffusion finite-difference schemes I. Constant coefficient in one dimension

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 455, Issue 1987, 1999, Pages 2371-2387

  Smith, Ronald ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

Diffusion equation; Finite difference scheme; Numerical method

Indexed keywords

EID: 33746454216     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0408     Document Type: Article

References (4)

1. Crandall, S. H. 1955 An optimum implicit recurrence formula for the heat conduction equation. J. Ass. Comput. Mach. 2, 42-49.
2. Crank, J. & Nicholson, P. 1947 A practical method for numerical integration of solutions of partial differential equations of heat conduction type. Proc. Camb. Phil. Soc. 43, 50-07.
3. Richtmyer, R. D. & Morton, K. W. 1967 Difference methods for initial-value problems, 2nd edn. New York: Wiley.
4. Saul'ev, V. K. 1958 On methods of higher accuracy in two-sided approximations to the solution of parabolic equations. Dokl. Akad. Nauk USSR 118, 1088-1090.