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中文摘要：
研究一类典型的伏尔泰拉积分方程的数值求解方法．通过数值差分离散积分方程，然后将积分方程演化为非线性代数方程组，通过迭代推进求解此类积分方程．分析这种求解方法的代数精度，证明此数值解法的精度高达△t^2阶，可以满足工程计算需要．通过数值仿真验证，数值解与解析解的误差为10^-5．如果采用更高阶的数值积分离散方式，可以获得更高阶精度．
英文摘要：
A new numerical solution is provided for Volterra integral equation of the second kind. The integral equation is discretized by numerical difference method and is then formulated as nonlinear algebraic equations, which is solved by iteration approach. Thus the numerical solution for this kind of Voherra Integral equation is provided. The accuracy of the proposed approach is analyzed and is proved to reach the order of △ t2 , which meets the need of engineering computation. A case study is provided to verify the feasibility of the method. The difference between the numerical solution and the analytical solution is about 10-5. If numerical differential method with higher order is applied to diseretize the integral equation, results of higher order accuracy will be obtained.
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