比例延迟微分方程均匀网格的BDF方法的收敛性及稳定性

摘要

研究在均匀网格下,比例延迟微分方程向后微分公式的收敛性及稳定性.在均匀网格下,将向后微分公式与线性插值相结合来求解比例延迟微分方程,给出相应的差分格式,证明该差分格式数值解的收敛阶为1;分析比例延迟微分方程向后微分公式的渐近稳定性;数值算例验证了理论结果.%The convergence and stability of backward differential formulas on uniform meshes for pantograph differential equations are dealt with.The backward differential formula (BDF) combined with a linear interpolation on uniform meshes is presented to solve pantograph differential equations.It is proved that the numerical solution convergent to the exact solution with order 1.The asymptotic stability of the BDF is investigated.Some numerical experiments are given to illustrate the theoretical results obtained.