【摘要】 针对二阶Fredholm积分微分方程,提出了一种新的有限差分配置法.该方法的关键思想在于利用中心差分和分片线性Lagrange插值函数,将奇异核分裂成有限项,并用分部积分克服了奇异性.通过分析,给出了对应的代数方程组,证明了代数方程组的解的存在唯一性和收敛性.通过多个数值算例验证了所给方法的有效性.更多还原

【Abstract】 In this paper,based on the central difference and piecewise linear Lagrange interpolation function,a finite differencecollocation method is presented for second-order linear Fredholm integro-differential equations. The corresponding algebraic equations are obtained. Three numerical examples are employed to illustrate the effectiveness of the proposed technique.更多还原