Numerical Computing Of Two Kinds Of Nonlinear Partial Integral Differential Equation

The integro-differential equation of parabolic type often occurs in application such as heat conduction in material with memory, comression of poro-viscoelastic media, nuclear reactor dynamics, ect. Theres are lots of documents of V.Thomee , W.Mclean , C.Lubich , L.Wahlbin , J .M.Sanz-Serna, E.G.Yanik, G.Fairweather in overseas and chuan-miao Chen,yuan-qing Huang,Da-Xu, Zhi-Zhong Sunin home. A lot of them use FEM; Spectral collocation methods; Spline collocation methods, ect.In the paper two kind of nonlinear partial integral differential equation is solved by numerical method, and the main results are described as follow:(1)A numerical method to solve the nonlinear sinusoidal vibration equation is presented, in which the explicit difference scheme is applied to discrete the space variable x and the time variable t separately and the trapezoidal rule is adopted to calculate the nonlinear integration;(2) The discrete scheme is given for a kind of nonlinear partial integral differential equation, in which the explicit difference scheme is applied to discrete the space variable x and the time variable t separately.The above methods have these advantages:(1) the solution for the nonlinear equation is unique; (2) the computational efforts is less;(3) the numerical solution has high precision.