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Runge-Kutta methods for numerical solutions of stochastic ordinary differential equations

Shi Qi-yan

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Abstract

In this paper,we give three Runge-Kutta numerical schemes for stochastic ordinary differential equations: explicit scheme,semi-implicit scheme and implicit scheme.The conditions of T-stability for the three Runge-Kutta numerical schemes are discussed and partial numerical results for a test linear equation are shown.

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What this paper is about

In this paper,we give three Runge-Kutta numerical schemes for stochastic ordinary differential equations: explicit scheme,semi-implicit scheme and implicit scheme.The conditions of T-stability for the three Runge-Kutta numerical schemes are discussed and partial numerical results for a test linear equation are shown.

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Available abstract

In this paper,we give three Runge-Kutta numerical schemes for stochastic ordinary differential equations: explicit scheme,semi-implicit scheme and implicit scheme.The conditions of T-stability for the three Runge-Kutta numerical schemes are discussed and partial numerical results for a test linear equation are shown.

Key concepts: Runge–Kutta methods, Mathematics, Explicit and implicit methods, Numerical methods for ordinary differential equations, Ordinary differential equation, Numerical stability, Exponential integrator, Scheme (mathematics)

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