Imperfect singular solutions of nonlinear equations and a numerical method of proving their existence
A new concept of "an imperfect singular solution" is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration.
numerical computation with guaranteed accuracy krawczyk-based interval validation method imperfect singular solutions extended systems