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

Stefan M. Filipov, Ivan D. Gospodinov, I. Faragó

Research output: Contribution to journalArticle

8 Citations (Scopus)

### 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 H1 semi-norm of the difference between itself and the initial value problem solution.

Original language English 10-15 6 Applied Mathematics Letters 72 https://doi.org/10.1016/j.aml.2017.04.002 Published - Oct 1 2017

### Fingerprint

Shooting Method
Two-point Boundary Value Problem
Projection Method
Boundary value problems
Initial Value Problem
Initial conditions
Initial value problems
Iteration
Boundary conditions
Auxiliary Function
Seminorm
Second-order Ordinary Differential Equations
Guess
Differential equation
Minimise
Ordinary differential equations
Differential equations

### Keywords

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

### ASJC Scopus subject areas

• Applied Mathematics

### Cite this

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

In: Applied Mathematics Letters, Vol. 72, 01.10.2017, p. 10-15.

Research output: Contribution to journalArticle

Filipov, Stefan M. ; Gospodinov, Ivan D. ; Faragó, I. / Shooting-projection method for two-point boundary value problems. In: Applied Mathematics Letters. 2017 ; Vol. 72. pp. 10-15.
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