Stochastic finite element based on stochastic linearization for stochastic nonlinear ordinary differential equations with random coefficients

  • Authors:

  • M. M. Saleh;I. L. El-kalla;M. M. Ehab

  • Affiliations:

  • Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Egypt;Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Egypt;Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Egypt

  • Venue:
  • NOLASC'06 Proceedings of the 5th WSEAS international conference on Non-linear analysis, non-linear systems and chaos
  • Year:
  • 2006

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Abstract

We propose an algorithm for solving stochastic nonlinear ordinary differential equations with random coefficients. This algorithm is based on stochastic linearization and solution of the linearized equation by stochastic finite element method. The deterministic coefficient of the nonlinear term is divided into n levels and the coefficient of the linearization at each level depends on the moments of the solution at the previous level. Numerical examples are illustrated to choose the optimum n levels for each problem.