Nonlocal boundary value problems for hyperbolic-schrodinger equations

This thesis consists of five chapters. First chapter is the introduction. Second chapter consists of three sections. A brief survey of all investigations in this area can be found in the first section. In the second section the main theorem about stability of the nonlocal boundary value problem for hyperbolic-Schrödinger equations in a Hilbert space is proved. In applications this abstract result permits to obtain the stability estimates for the solution of the difference schemes for hyperbolic- Schrödinger equations. It is given in the last section. Third chapter consists of two sections.The stable first and second order of accuracy difference schemes approximately solving the nonlocal boundary value problem for hyperbolic- Schrödinger equation in a Hilbert space H with self-adjoint positive definite operator A are presented. The stability estimates for the solutions of the difference schemes of the mixed type boundary value problems for hyperbolic-parabolic equations are obtained. Fourth chapter is the applications. The first and second order of accuracy difference schemes are studied. A matlab program is given to conclude that the second order of accuracy is more accurate. The figures and table are included. Fifth chapter is the conclusions.