The Solution of Initial Value Problems Using Interval Arithmetic. Formulation and Analysis of an Algorithm

摘要

Initial value problems are considered for systems of M ordinary differential equations, where M or = 1. The problem of enclosing the solution numerically for arbitrary values of the independent variable t is addressed. The initial value is not exactly known, but is only known to be contained in a given initial value set. The corresponding set of solutions for arbitrary t is enclosed. All possible sources of errors, including rounding errors due to the finite precision of a computer are taken into account. A numerical method for solving the aforementioned problem is formulated.