Symbolic Algorithm for Mixed Interpolation Problem. An Application to Linear Boundary Value Problems

      Аннотация: Symbolic computation is playing the central role to solve the mathematical equations, especially the boundary value problems for differential equations. The symbolic computation is an important tool in scientific field, which is also known as computer algebra. In twenty-th century, the science and technology had a very swift progress in various fields, especially in computing, the subfield of scientific and technological computing. One of the biggest successes in the research of symbolic computation is the development of significant software systems. In some applications, for example the orbit problems, quantum mechanical problems and solving differential and integral equations (second kind of Fredholm) numerically, it is appropriate to consider mixed interpolation instead of polynomial interpolation. Polynomial interpolation problem will become a special case of the mixed interpolation problem if we replace the certain terms of the mixed interpolation problem. This book extends the theory of mixed interpolation to the situation where the interpolation conditions are not only of the functional or differential type, but also of the integral type.

Ключевые слова: Mixed Interpolation, Symbolic Algorithm, Boundary value problems, MAPLE, Intergro-differential Algebra