I know that there is an initial guess of initial value to solve a BVP using shooting method but it is obtained from literature that bisection method to find the exact initial value, my question is how bisection method is used to find exact initial value of a BVP.
Please reply.
Thank you
Is this question about ordinary differential equations or partial differential equations? Many years ago I developed some software to use the shooting method to estimate initial conditions and parameter values for nonlinear ordinary differential equations. My application was to estimate parameter values in the governing equations using observations on system states at various times. The software generally followed the so called "Method of Complementary Functions" or the "Perturbed Particular Solutions Method". Theory behind methods can be found in the published works of Richard Bellman, Robert Kalaba, Harriet Kagiwada, (Rand Corporation) and Bart Childs (Texas A&M, University).
You may refer the following paper entitled
shooting method in solving boundary value problem https://www.arpapress.com/Volumes/Vol21Issue1/IJRRAS_21_1_02.pdf
see
Using the shooting method to solve boundary-value problems involving nonlinear coupled-wave equations
Y. H. Ja
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