Rossokhata N. Numerical-analytical methods for modeling of biosensor systems based on semiconductors

The thesis deals with the theoretical-experimental investigation of mathematical models of biosensors based on semiconductors, and described by nonlinear second order partial differential equations with transmission condition; as well as development of numerical methods preserving analytical properties of exact solution for modeling of processes which incorporate Schredinger equation. The existanse and uniqueness of exact solution is investigated, numerical techniques are developed to find approximate solution. The exponential convergence rate of functional-discrete technique is proved for both linear and nonlinear eigenvalue problems. Qualitative results about asymptotics for exact eigenvalues are established. Numerical examples to support the theory and illustrate the effectiveness of proposed approaches are presented.