Numerical solution of symmetric positive differential equations
HTML articles powered by AMS MathViewer
- by Theodore Katsanis PDF
- Math. Comp. 22 (1968), 763-783 Request permission
Abstract:
A finite-difference method for the solution of symmetric positive linear differential equations is developed. The method is applicable to any region with piecewise smooth boundaries. Methods for solution of the finite-difference equations are discussed. The finite-difference solutions are shown to converge at essentially the rate $O({h^{1/2}})$ as $h \to 0,h$, being the maximum distance between adjacent mesh-points. An alternate finite-difference method is given with the advantage that the finite-difference equations can be solved iteratively. However, there are strong limitations on the mesh arrangements which can be used with this method.References
- K. O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958), 333–418. MR 100718, DOI 10.1002/cpa.3160110306 C. K. Chu, Type-Insensitive Finite Difference Schemes, Ph.D. Thesis, New York University, 1958. T. Katsanis, Numerical Techniques for the Solution of Symmetric Positive Linear Differential Equations, Ph.D. Thesis, Case Institute of Technology, 1967.
- Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
- R. H. Macneal, An asymmetrical finite difference network, Quart. Math. Appl. 11 (1953), 295–310. MR 0057631, DOI 10.1090/qam/99978
- Samuel Schechter, Quasi-tridiagonal matrices and type-insensitive difference equations, Quart. Appl. Math. 18 (1960/61), 285–295. MR 114309, DOI 10.1090/S0033-569X-1960-0114309-X
- Jean Céa, Approximation variationnelle des problèmes aux limites, Ann. Inst. Fourier (Grenoble) 14 (1964), no. fasc. 2, 345–444 (French). MR 174846
- Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0098966
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Math. Comp. 22 (1968), 763-783
- MSC: Primary 65.65
- DOI: https://doi.org/10.1090/S0025-5718-1968-0245214-9
- MathSciNet review: 0245214