演講者： Tzon-Tzer Lu (呂宗澤) (國立中山大學應用數學系)

標題：Adomian Decomposition Method for First Order PDEs

時間：12月10日下午02點00分

地點：校本部第二綜合大樓8樓 B808 教室

摘要： In this talk we like to demonstrate the full power of Adomian decomposition method (ADM). ADM has the capability to obtain three different types of solutions, namely explicit exact solution, analytic solution and semi-analytic solution. When a closed form solution exists, ADM is possible to capture this explicit solution, while most of the numerical methods can only get approximation, not exact solution. We will illustrate the superior of ADM to solve the prototype nonlinear PDEs, i.e. the inviscid and viscous Burgers' equations with source term and parameter. Next, we employ the standard ADM and ADM with integration factor to compute explicit closed form solutions of first order partial differential equations with unprescribed initial conditions, and even with parameters. These symbolic features are those numerical methods fail to do. Our examples include linear/nonlinear, constant/variable coefficients, scalar/system and homogeneous/nonhomogeneous equations etc. Furthermore, the method of characteristics is also tested and compared with these two ADM methods. ADM itself is a computational method for solution, while the method of characteristics needs assistance from other numerical methods to solve differential equations of characteristic curve and solution on it. So we conclude that ADM is far more powerful than existing methods.