## Abstract

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations (ODE’s) and then define an optimization problem related to it. The new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional*E* (we define in this paper) for the approximate solution of the ODE’s problems.

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Effati, S., Kamyad, A.V. & Farahi, M.H. A new method for solving the nonlinear second-order boundary value differential equations.
*Korean J. Comput. & Appl. Math* **7, **183–193 (2000). https://doi.org/10.1007/BF03009936

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### AMS Mathematics Subject Classification

- 34B15
- 49J15

### Key Word and Phrases

- ODE’s
- measure theory
- optimal control
- linear programming