A Class Of Nonlinear Neutral Stability Variable Delay Integral Equations

Delay differential equations(DDEs) plays a very significant role in a wide variety, for exam-ple Physics, Engineering, Biology, Medical Science, Economic fields and so on. Its stability oftheoretical solution and numerical solutions have been widely studied by many authors. Mean-while, neutral delay differential equations(NDDEs) is special subclass of DDEs, there havemany conclusions and studies about the stability of the theoretical and numerical solutions.Recently, the stability of theoretical and numerical methods for NDDEshave been widelystudied. However, there are few works about theoretical stability and numerical stability fornonlinear neutral delay integration differential equations(NDIDEs). Therefore, it is importantto study the stability of the neutral delay integration differential equations(NDIDEs). Thispaper will study the stability of a class of nonlinear neutral variable delay integration differentialequations.Firstly, we study the theoretical stability of solutions for nonlinear neutral variable delayintegro-differential equations. Secondly, we study the numerical stability of solutions for non-linear variable neutral delay integro-differential equations. And in the given conditions, we studythe stability of the linear multi-step method and Runge-Kutta(RK) method for solving a class ofnonlinear neutral variable delay integro-differential equations. and we prove the correspondingresults.