中文摘要：

1引言 自然界许多物理现象都可用对流扩散方程来描述，如质量、能量以及动量守恒问题等．实际应用问题中的对流扩散方程往往比较复杂，难以求出精确解，因此研究其数值求解方法具有十分重要的意义．

英文摘要：

The unsteady convection-diffusion equation is converted to a linear diffusion equation by the exponential transformation. Then a Pade approximation compact finite volume scheme is proposed by the 4th-order Pad5 compact finite volume scheme for spatial derivatives and a Pade[2/2] approximation method for time variable. The new scheme has the fifth order accuracy in time and the fourth order accuracy in space, and is proved to be unconditionally stable. The compact high-order finite volume scheme posses inherent conservation of the equation and high order accuracy within small stencils. Finally, some numerical examples are presented to verify the validity of the new scheme, as well as the advantages of high accuracy and high resolution in dealing with the boundary layer problems or locally large gradient problems.