Cubically convergent method for solving a standard boundary value problem

Rafał Palej

Abstrakt

The paper presents a cubically convergent method for solving a standard boundary value problem consisting of n coupled first-order differential equations and n boundary conditions. The idea of the presented method is based on the shooting method using the expansion of the desired function into Taylor’s series including second-order derivatives. Effective use of the iteration formula requires introduction of sensitivity functions and their derivatives. In each iteration, the initial problem, composed of n(1+ n1+ n21 ) first-order differential equations, must be solved, where n1 signifies the number of unknown parameters. The convergence of the presented method has been illustrated on an example.

Słowa kluczowe: shooting method, sensitivity functions, derivatives of sensitivity functions, cubic convergence
References

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Palej R., Cubically convergent method for nonlinear equation systems, Czasopismo Techniczne 4-M/2011/B, Wydawnictwo PK, Kraków 2011.

Rao S.S., Applied Numerical Methods for Engineers and Scientists, Prentice Hall, New Jersey 2002.

Dahlquist G., Björck Å., Numerical Methods in Scientific Computing, Volume I, SIAM, Philadelphia 2008.