No. 27 (286), issue 13Pages 16 - 23 #
The Method of the Integral Equations to Construct the Green's Function

Yu.S. Asfandiyarova, V.I. Zalyapin, Ye.V. KharitonovaLinear differential operator and the system of the boundary conditions were considered. The boundary conditions are linear and linear independent functionals. The Green's function for the defined by this operator and functionals boundary problem was build as solution of the Fredholm's integral equation of the second kind. Characteristics of the Fredholm's equation was defined by the Green's function of the auxiliary problem. Resulting Green's function makes it possible to solve both direct (the problem of finding solutions) and inverse (the problem of finding the right part of the equation from the experimentally obtained solution) problems. The numerical algorithm to solve boundary problem and inverse problem was build on the basis of the proposed method and tested .

Full text- Keywords
- linear boundary problem, Green's function, integral equations.
- References
- 1. Shestakov A.L. Dynamic Error Correction Method. IEEE Transactions on Instrumentation and Measurement, 1996, vol. 45, no. 1, pp. 250-255.

2. Sansone D. Ordinary Differential Equations, vol.1. Мoscow, IL, 1953. (in Russian)

3. Ilyin V.A., Moiseev Ye.I. Differential and Difference Form for the Nonlocal Boundary Problem of the Sturm-Liouville's Operator. DAN USSR, 1986, vol. 291, no. 3, pp. 534-539. (in Russian)

4. Tikhomirov V.M. Some Problems of the Approximation Theory. Мoscow, MSU, 1976. 305 p. (in Russian)

5. Zalyapin V.I., Kharitonova H.V., Yermakov S.V. Inverse problem of the measurements theory. Inverse Problems, Design and Optimization Symposium, Miami, Florida, USA, 2007, pp. 91-96.

6. Asfandiyarova Yu.S., Zalyapin V.I. The Green's Function of the Linear Boundary Problem with Non-local Data. Proceedings of the Lobachevskii's Mathematical Center: Kazan Mathematical Society, 2009, vol. 39, pp. 128. (in Russian)

7. Neimark M.A Linear Differential Operators. Moscow, Nauka pub., 1969, 528 p. (in Russian)