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2007•Journal of Chengdu University of Information TechnologyRequires access

Euler methods for numerical solution of stochastic ordinary differential equations

HU Jian-cheng

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Abstract

Based on the well-established numerical methods for the deterministic ordinary differential equations the Euler method is applied to a scalar autonomous stochastic ordinary differential equation and three Euler numerical schemes are given: explicit scheme;semi-implicit sheme and implicit scheme.One type of stability of the Euler method,T-stability,is considered.Numerical results of a linear test equation show that the Euler method for solving SODEs is meaningful.

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What this paper is about

Based on the well-established numerical methods for the deterministic ordinary differential equations the Euler method is applied to a scalar autonomous stochastic ordinary differential equation and three Euler numerical schemes are given: explicit scheme;semi-implicit sheme and implicit scheme.One type of stability of the Euler method,T-stability,is considered.Numerical results of a linear test equation show that the Euler method for solving SODEs is meaningful.

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Available abstract

Based on the well-established numerical methods for the deterministic ordinary differential equations the Euler method is applied to a scalar autonomous stochastic ordinary differential equation and three Euler numerical schemes are given: explicit scheme;semi-implicit sheme and implicit scheme.One type of stability of the Euler method,T-stability,is considered.Numerical results of a linear test equation show that the Euler method for solving SODEs is meaningful.

Key concepts: Explicit and implicit methods, Euler method, Backward Euler method, Semi-implicit Euler method, Mathematics, Ordinary differential equation, Numerical stability, Euler equations

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