STABILITY OF AN IMPLICIT METHOD FOR THE NUMERICAL SOLUTION OF ABEL TYPE ALGEBRAIC EQUATIONS

Author (s) : Dr.T.Sakthivel, V.R Manimaran ,B.Venkatachalam, V.Jothilakshmi

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Abstract :
This article is devoted to a study of the properties of an implicit method for Abel type algebraic equations. An Abel type integral equation with stiff components is used for examining the properties of this method, and stability domains are constructed. Numerical calculations confirming the results obtained are performed. A fractional “stiff” problem is proposed to study the stability of the mathematical objects considered. a system of simultaneous generalized first and second kind Abel integral equations is considered. Such systems can be represented as an integral equation with an identically singular matrix in front of the main part, which will be called an integral-algebraic equation (IAE) of the Abel type or an integral-algebraic equation with a weak diagonal singularity in the kernel

Keywords : Abel type integral-algebraic equations, Volterra integral equations, k-step methods, stiff problem, stability domains

Conference Date : 30/08/2019

Pages : 222

Paper ID : 19213