Mixed algorithm for solving boundary value problem
Abstract
Symbolic computation has been applied to Runge-Kutta technique in order to solve two-point boundary value problem. The unknown initial values are considered as symbolic variables, therefore they will appear in a system of algebraic equations, after the integration of the ordinary differential equations. Then this algebraic equation system can be solved for the unknown initial values and substituted into the solution. Consequently, only one integration pass is enough to solve the problem instead of using iteration technique like shooting-method. This procedure is illustrated by solving the boundary value problem of the mechanical analysis of a liquid storage tank. Computation was carried out by MAPLE V. Power Edition package.
References
[2] D.B. Meade et al. The shooting technique for the solution of two-point boundary value problems. Maple Tech, 3(1): 85, 1996.
[3] B.A. Finlayson. Nonlinear Analysis in Chemical Engineering. McGraw- Hill, New York, 1980.
[4] J. Zhang. Symbolic computation on complex polynomial solution of differential equations. J. Symbolic Computation, 22: 345, 1996.
[5] R.D. Mills. Slope retention technique for solving boundary-value problem in differential equations. J. Symbolic Computation, 13: 59, 1992.
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