### Abstract

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 H^{1} semi-norm of the difference between itself and the initial value problem solution.

Original language | English |
---|---|

Pages (from-to) | 10-15 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 72 |

DOIs | |

Publication status | Published - Oct 1 2017 |

### Fingerprint

### Keywords

- H semi-norm
- Shooting-projection method
- Two-point boundary value problem

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Applied Mathematics Letters*,

*72*, 10-15. https://doi.org/10.1016/j.aml.2017.04.002

**Shooting-projection method for two-point boundary value problems.** / Filipov, Stefan M.; Gospodinov, Ivan D.; Faragó, I.

Research output: Contribution to journal › Article

*Applied Mathematics Letters*, vol. 72, pp. 10-15. https://doi.org/10.1016/j.aml.2017.04.002

}

TY - JOUR

T1 - Shooting-projection method for two-point boundary value problems

AU - Filipov, Stefan M.

AU - Gospodinov, Ivan D.

AU - Faragó, I.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - H semi-norm

KW - Shooting-projection method

KW - Two-point boundary value problem

UR - http://www.scopus.com/inward/record.url?scp=85018474005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018474005&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2017.04.002

DO - 10.1016/j.aml.2017.04.002

M3 - Article

AN - SCOPUS:85018474005

VL - 72

SP - 10

EP - 15

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -