The numerical solution of ordinary differential and differential algebraic equations

The book is devoted to the numerical solution of problems with the initial conditions for ordinary differential and differential-algebraic equations.
Explicit and implicit, classmate and multi -step methods are considered, including new original methods. Particular attention is paid to solving tough problems (including using special obvious methods), as well as solving the differential-algebraic problems of higher indices. Along with theoretical results, the results of solving test problems are given and issues of programmatic implementation of numerical methods are considered.
For everyone who is interested in numerical methods for solving differential and differential-algebraic equations.
Setting the problem of the Koshi for ODU and DAU systems, various tasks and methods for solving them
clear methods of Runge-Kutta for non-profitable tasks
Recommendations for choosing optimal coefficients
Two ways to build invested steam Methods with error assessment
Non-step methods of low accuracy
Theoretical and experimental results about convergence of the methods of Runge-Kutta
Simplified conditions of the order
specific methods with minimized errors
implicit methods, implicit methods. with increased accuracy in solving tough problems and DAU.
Non -step and multi -step methods with advanced stability areas