Error Analysis Of Implicit-explicit Linear Multistep Methods And Implicit-explicit One-leg Methods For Stiff Initial Value Problems

In many applications, such as automatic control, atmospheric chemistry andspatial discretization of initial boundary value problems of partial diferential equa-tions, etc, some large systems of ordinary diferential equations(ODEs) with bothstif and nonstif parts are often encountered. In order to make the computationmore efcient, we often adopt implicit-explicit methods, i.e. the stif parts are inte-grated implicitly and the nonstif parts are integrated explicitly.Now, the popular implicit-explicit methods mainly include two classes: theimplicit-explicit linear multistep methods and the implicit-explicit Runge-Kuttamethods. In this paper, our interest pours into studying the convergence of theimplicit-explicit linear multistep methods and the implicit-explicit one-leg methodsfor two popular classes of stif initial value problems. The full text is composed offour chapters.In Chapter1, we introduce briefly the research background, the current researchsituation, the previous relative results about implicit-explicit methods and the mainwork of this paper.In Chapter2, we introduce some related preliminary knowledge and two classesof initial value problems.In Chapter3, the errors of the implicit-explicit linear multistep methods andimplicit-explicit one-leg methods for solving the first class of initial value problemsare analyzed. Some numerical experiments confirm the obtained convergence results.In Chapter4, the errors of the implicit-explicit linear multistep methods andimplicit-explicit one-leg methods for solving the second class of initial value problemsare analyzed. Some numerical experiments confirm the obtained convergence results.