Stability Of Numerical Methods For Differential Systems With Distributed Delays

Delay differential equation is a class of functional differential equations.It is hard to obtain analytical solutions of explicit form,therefore,it is necessary to study numerical solutions of delay differential equations.In this thesis,stability of numerical methods is studied for delay differential equations with distributed delays.The weak delay-dependent stability of several numerical methods are investigated.In addition,several numerical experiments are given to illustrate the main results ·Main contributions of the thesis are as follows:In chapter one and two,the background and the recent results in the literature are reviewed;In chapter three,the weak delay-dependent stability of Pouzet-type Runge-Kutta methods is studied.Several conditions are obtained using the argument principle.Furthermore,an algorithm is given to check weak delay-dependent stabil-ity conditions.Numerical examples are provided to certify the effectiveness of the acquired results.In chapter four,the weak stability of linear multi-step methods is studied for delay differential equations with distributed delays.Some weak delay-dependent stability criteria are derived by the argument principle.In addition,an algorithm is offered to check the weak delay-dependent stability conditions.Numerical examples are provided to demonstrate the effectiveness of the obtained results.In chapter five,Rosenbrock methods are applied to solve delay differential e-quations with distributed delays.With the compound integral formula,several weak delay-dependent stability conditions of Rosenbrock methods are derived by means of the argument principle.Moreover,an algorithm,is provided to examine the con-ditions.Numerical examples are given to verify the effectiveness of the achieved results.