2011/09/04 by Alexander Lozovskiy, Lozovskiy, Alexander
Engineering · Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Heat Transfer and Mathematical Modeling #Material Science and Thermodynamics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1109.0703
openalex publication_date 2011/09/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A new numerical method for solving a scalar ordinary differential equation with a given initial condition is introduced. The method is using a numerical integration procedure for an equivalent integral equation and is called in this paper an integrating method. Bound to specific constraints, the method returns an approximate solution assuredly within a given tolerance provided by a user. This makes it different from a large variety of single- and multi-step methods for solving initial value problems that provide results up to some undefined error in the form O(hk), where h is a step size and k is concerned with the method's accuracy. Advantages and disadvantages of the method are presented. Some improvements in order to avoid the latter are also made. Numerical experiments support these theoretical results.