Using FEM–RVT technique for solving a randomly excited ordinary differential equation with a random operator

The technique of stochastic finite element (SFEM) which is the finite element technique FEM adapted to stochastic problems can be re-described to use random variable transformation technique RVT. A new FEM–RVT technique was successfully used in solving stochastic problems with random excitation [M. El-Tawil, W. El-Tahhan, A. Hussein, A proposed technique of SFEM on solving ordinary random differential equation, J. Appl. Math. Comput. 161 (2005) 35–47].In this paper, the technique is adapted to solve a randomly excited differential equation with a random operator. The technique shows high accuracy when solving a case study compared with the exact solution. Finally a problem with unknown exact solution is solved using this technique.