Numerical Solution Methods Of Volterra Type Integral Differential Equations

In today's rapid development of science and technology,nonlinear integro-differential equations have become one of the main tools in various fields such as mechanics and engineering.These equations can be applied to many practical prob-lems,such as electromagnetics,fluid dynamics,oscillation theory,polymer rheology,biomechanics,etc.Volterra-type equations are one of the most important branches of integro-differential equations which are widely used in medicine and population growth models.The nature of better memory of Volterra-type equations has attract-ed much attention in physics,biology,chemistry and other disciplines.Therefore,obtaining the numerical solution of integro-differential equations accurately and quickly has become a hot issue.Supported by the theory of reproducing kernels,this paper is studied the nu-merical solutions of two types of nonlinear Volterra-type integro-differential equa-tions.Firstly,the homotopy perturbation method is used to linearize the nonlinear term.Then the corresponding reproducing kernel space is constructed for differ-ent models,and the reproducing kernel function is obtained.Next,a simplified reproducing kernel method is applied to solve the model in the kernel space.Mean-while,we provide the convergence analysis of the proposed method.Finally some numerical examples to verify the feasibility of the method are given.