Sinc Method For The Partial Integro-differential Equation On Unbounded Domain

We often need to solve the integro-differential equation of parabolic type in heat conduction in materials with memory, population dynamics, Compression of porous viscoelastic medium, nuclear reactor dynamics problems etc. There have a lot of work on the numerical solutions of such equation both at home and abroad. In this paper the full discrete Sine scheme on unbounded domain for integro-differential equation of parabolic type is considered. The Euler method was applied in the time direction, and the Sine method was used to discrete the space direction. The Sine function is a kind of wavelet approximation, and we does not need to consider the boundness of time and space by using the Sine method. The numerical examples of ordinary differential equations and partial differential equations showed that the method has good stability and convergence.