be the boundary value problem. Let y(t1; a) denote the solution of the initial value problem
Define the function F(a) as the difference between y(t1; a) and the specified boundary value y1.
If the boundary value problem has a solution, then F has a root, and that root is just the value of y'(t0) which yields a solution y(t) of the boundary value problem.
The usual methods for finding roots may be employed here, such as the bisection method or Newton's method.
References
Josef Stoer and Roland Bulirsch. Introduction to Numerical Analysis. New York: Springer-Verlag, 1980. (See Section 7.3.)
A topological shootingmethod and the existence of kinks of the extended Fisher-Kolmogorov equation.
L.A. Peletier and W.C. Troy, A topological shootingmethod and the existence of kinks of the Extended Fisher-Kolmogorov equation, preprint of the Mathematical Institute, University of Leiden, The Netherlands.
Peletier and W. Troy, A topological shootingmethod and the existence of kinks of the Extended Fisher-Kolmogorov equation, Topological Methods in Nonlinear Analysis 6 (1995), 331--355.
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