Stability Analysis Of Runge-Kutta Methods For Nonlinear Multi-Variable Delay Integro-Differential Equations

Delay integro-differential equations arise widely in the fields of physics, biology, medicine, chemistry, economics, ecology, control theory and so on. Considering that the analytical solutions of delay integro-differential equations are difficult to be obtained, the investigation of numerical methods is very meaningful. Moreover, stability is one of basilic indexes to weigh the validity of a method in numerical analysis, so the research of stability of numerical methods is the main task in numerical analysis. The present paper is devoted to the stability analysis of Runge-Kutta methods for nonlinear delay integro-differential equations, and is organized as follows:In the first chapter, we introduce application background and research background of delay differential equations, and recall the history of its study of analytical solutions and numerical solutions. The main innovations of this article are introduced.In the second chapter, we introduce the research object of this article-qualitative analysis of nonlinear multi-variable delay integro-differential equations.In the third chapter, the Runge-Kutta methods are extended and applied to nonlinear multi-variable delay integro-differential equations, some stability conditions are abtained.In the fourth chapter, the ERK methods are applied to several nonlinear delay integro-differential equations, from the Angle of application, verify the numerical sta-bility of the third chapter, the numerical test results show that this calculation method is effective in practical application.In the last, this paper made a summary, prospected the future research direction.