Finite analytic numerical method for two-point boundary value problems of ordinary differential equations. (English) Zbl 0708.65074
The authors consider a method for solving boundary value problems for ordinary differential equations which is called the “finite analytic numerical method”. The basic idea is the incorporation of the local analytic solution of the governing equation on short subintervals in the numerical solution of the problem.
Of course the equation has to be simplified before. The technique is developed for both linear and nonlinear second-order differential equations. Several examples are solved and the numerical results are compared with results of finite difference approximations and shooting algorithms. It turns out that difference schemes are specializations of the finite analytic and that the accuracies attainable are comparable.
Of course the equation has to be simplified before. The technique is developed for both linear and nonlinear second-order differential equations. Several examples are solved and the numerical results are compared with results of finite difference approximations and shooting algorithms. It turns out that difference schemes are specializations of the finite analytic and that the accuracies attainable are comparable.
Reviewer: H.Weber
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
finite analytic numerical method; nonlinear second-order differential equations; numerical results; finite difference approximations; shooting algorithmsReferences:
| [1] | Cryer, C. W., The numerical solution of boundary value problems for second order functional differential equations by finite differences, Numer. Math., 20, 288-299 (1973) · Zbl 0247.65053 |
| [2] | Holt, Y. F., Numerical solution of nonlinear two-point boundary value problems by finite difference method, Comm. ACM, 7, 363-373 (1964) · Zbl 0123.11805 |
| [3] | Ciarlet, P. G.; Schultz, M. H.; Varga, R. S., Numerical methods of high order accuracy for nonlinear boundary value problems, Numer. Math., 13, 51-77 (1967) · Zbl 0181.18603 |
| [4] | Bellman, R. E.; Kalaba, R. E., Quasilinearization and Nonlinear Boundary Value Problems (1965), Elsevier: Elsevier New York · Zbl 0139.10702 |
| [5] | Alien, R. C.; Scott, M. R.; Wing, G. M., Solution of certain class of nonlinear two point boundary value problems, J. Comput. Phys., 4, 250-257 (1969) · Zbl 0202.16001 |
| [6] | Li, P.; Chen, C. J., The finite differential method—A numerical solution to differential equation, (Proceedings of the Seventh Canadian Congress of Applied Mechanics. Proceedings of the Seventh Canadian Congress of Applied Mechanics, Sherbrooke, May 27-June 1 (1979)), 909-910 |
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