Numerical Algorithms For Two Types Of Parabolic Partial Differential Equations

Heat conduction equation as a typical parabolic partial differential equation is widely used in many fields.Recently a lot of mathematical models,especially in financial mathematics,often appear as option models,which makes many scholars very keen on its research.It is difficult to get the exact analytical solution of this kind of equation due to the complexity of practical problems.The research is very important for developing the numerical theories of heat conduction theories of heat conduction equation as well as solves further practical problems.In this paper,the numerical solutions of two kinds of parabolic partial differen-tial equations,namely,parabolic partial differential equation with delay term and parabolic partial differential equation with disturbance delay,are discussed.A new reproducing kernel space is established by the definition of an inner produce with a delay form.At the same time,the calculation formula of the reproducing ker-nel function is given.Fxirthermore,the numerical algorithm of two type parabolic partial differential equations are obtained,and the convergence and error estima-tion are given.Finally,the correctness and effectiveness of the algorithm is verified by some concrete heat conduction equation examples using Mathematica software.The numerical experiments results show that the algorithm proposed in this paper is suitable for obtaining high-precision numerical solutions.