Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory
The paper deals with global, rigorous and realistic bounds for the solutions of initial value problem for dissipative differential equations. The authors use one-sided Lipschitz conditions to obtain the local and global errors. A new existence theorem is proved giving conditions under which an initial value problem has a solution that remains close to a given approximation. By methods of interval analysis, logarithmic norms and differential inequalities a set of sufficient conditions is presented that give global bounds for all times.
scientific article; zbMATH DE number 627655
scientific article