Abstract
This paper introduces the better algorithms to obtain refined
initial guesses with shooting method for solving boundary value problems
(BVPs). Each boundary value problem (BVP) is reformulated as a system
of equations i.e. initial value problems (IVPs) with one unknown initial
conditions. Afterwards, the system of equations is solved using newly developed shooting method [2]. This article proposes efficient initial guess
algorithms rather than conventional Newton method to approach the adjoint terminal conditions rapidly. We enhanced the efficiency and accuracy
of shooting method by first improving our initial guess and then solving
the problem iteratively. The suggested technique is applied to solve different nonlinear higher order boundary value problems. The results indicate
that the proposed method is more efficient and accurate as compared to
build-in-functions which is being used in MATLAB.
Shumaila Javeed, Assiya Shabnam, Dumitru Baleanu. (2019) An improved shooting technique for solving boundary value problems using higher order initial approximation algorithms, Punjab University Journal of Mathematics, Volume 51, Issue 11.
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