A Repriducing Kernel Method For Three-point Boundary Value Problems Of Partial Differential Equations

With the development of science and technology,multi-order partial differential equation plays a very important role in mathematics,physics,chemistry and other disciplines.This kind of equation is widely used in solving many practical problems,such as chemical engineering,thermal elasticity,groundwater flow and population dynamics,which attracted many scholars to research deeply.In this paper,we apply the theory of reproducing kernel and the knowledge of linear operators to solve the third order partial differential equations with three point boundary values.Two effective numerical algorithms are obtained.Firstly,the reproducing kernel spaces are constructed according to the characteristics of the model equation.The approximate solution of the model equation is obtained by using the traditional reproducing kernel method,and the feasibility of the method is demonstrated by three numerical examples.Next,the algorithm is improved by using the optimization method,which eliminates the Smith orthogonalization process,effectively improves the accuracy,and proves the existence,uniqueness and uniform convergence of the understanding.Finally,the feasibility and effectiveness of the optimization method are verified by comparing with the previous three numerical examples.