Struggling with complex differential equations? This paper introduces a technique for automatically solving initial value problems for sets of ordinary differential equations. A key feature is a criterion for selecting the order of approximation, aiming to maximize step size and reduce solution time. The described criterion is based on the selection of the order of approximation. The program embodying the techniques includes an option for handling "stiff" differential equations. This automated approach streamlines the integration process, offering a valuable tool for scientists and engineers across diverse fields. The program embodying the techniques appears in Algorithm 407.
Published in Communications of the ACM, this article aligns with the journal's focus on computer science and programming. By presenting an algorithm for automatic integration, the paper contributes to the development of computational tools for solving mathematical problems relevant to computer science and other scientific domains.