Stability domains of an implicit method for the numerical solution of Abel type integral algebraic equations
O.S. Budnikova1,2, M.N. Botoroeva1,2, G.K. Sokolova1,2
1Irkutsk State University, Irkutsk, Russia
2Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia
Keywords: Abel type integral-algebraic equations, Volterra integral equations, k-step methods, stiff problem, stability domains
Abstract
This article is devoted to a study of the properties of an implicit method for Abel type integral algebraic equations. An Abel type integral equation with stiff components is used for examining the properties of these methods and the stability domains are constructed. Numerical calculations confirming the results obtained are performed. In this article, a fractional “stiff” problem is proposed to study the stability of the mathematical objects considered.
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