Shooting-projection method for two-point boundary value problems

This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial...

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Bibliographic Details
Published in:Applied mathematics letters 2017-10, Vol.72, p.10-15
Main Authors: Filipov, Stefan M., Gospodinov, Ivan D., Faragó, István
Format: Article
Language:English
Subjects:
[formula omitted] semi-norm
Shooting-projection method
Two-point boundary value problem
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Summary:This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H1 semi-norm of the difference between itself and the initial value problem solution.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2017.04.002