Convergence of numerical solutions to stochastic pantograph equations with Markovian switching

Abstract: In this paper, a class of stochastic pantograph equations with Markovian switching is considered. The main purpose is to investigate the convergence of the Euler method of the equations. It is proved that the Euler approximation solution converge to the analytic solution in probability under weaker conditions. An example is provided to illustrate our theory. [Copyright &y& Elsevier]