Error Estimate Of Block-centered Finite Difference Method For A System Of Parabolic Differential Equations

We give a new set of block-centered finite difference schemes for the system of parabolic equations, and design two finite difference methods. One is backward-in-time, the other is forward-in-time. We mainly discuss the first method, give its error estimates and the main theorems, which show the method is suitable for computing ,and has good approximate accuracy.The thesis is consist of three chapters as shown below.Chapter one introduces the research background of the block-centered finite difference method and the situation of schistosomiasis model.Chapter two is composed of three sections.Section one gives convergence theorems of One-dimensional elliptic and parabolic equations with initial boundary value condition.Section two gives the notations , lemmas and discrete schemes of the system of parabolic equations.Section three gives the error estimates and the main results.Chapter three is composed of four sections.Section one introduces the schistosomiasis model: two-dimensional case.Section two is the notations and lemmas.Section three gives three discrete schemes of the parabolic equations.Section four discusses the error estimates and the main results.