中文摘要：

研究了一类具有年龄结构的种群扩散系统反问题的数值解.对原系统变形后建立了具有高精度的四阶Pade差分格式来计算种群的密度和扩散系数,该格式的截断误差为O（τ2＋h4）并且无条件稳定,所得结果能更准确的描述种群密度和扩散系数.数值算例验证了方法的精确性和可靠性.

英文摘要：

Numerical method for an inverse problem of age-dependent population systems with diffusion is studied in this paper. A forth-order Pade numerical algorithm is proposed to calculate the population and the diffusion coefficient after a series of original form changes. The forth-order Pade numerical algorithm is unconditionally stable and has a truncation error of O（r2 ＋h4）. The obtained results can reflect the population and the diffusion coefficient more accurately. Finally, a numerical example is presented to demonstrate the efficiency and accuracy of the numerical method.