Asymptotic behavior of solutions to a Volterra integro-differential equation
The authors study the asymptotic behaviour of solutions of Volterra integro-differential equations of the form \((*)\quad y'(t)=\gamma y(t)+\int^{t}_{0}(\lambda +\mu t+\nu s)y(s)ds,\) \(y(0)=1\), \(t\geq 0\), where \(\gamma\), \(\lambda\), \(\mu\) and \(\nu\) are real parameters such that \(\mu +\nu \neq 0\), through the related ordinary differential equations \(y\prime''=\gamma y''+(\lambda +(\mu +\nu)t)y'+(2\mu +\nu)y.\) They obtain sufficient conditions for the boundedness of the exact solution of (*). This enables them to compare the exact solution with the approximate solutions of (*) resulting from the application of reducible linear multistep methods and modified multilag methods. A numerical example is given to illustrate their results.
scientific article; zbMATH DE number 4118957