Rounding Error in Numerical Solution of Stochastic Differential Equations
نویسندگان
چکیده
The present investigation is concerned with estimating the rounding error in numerical solution of stochastic differential equations. A statistical rounding error analysis of Euler’s method for stochastic differential equations is performed. In particular, numerical evaluation of the quantities EjXðtnÞ2 Ŷnj and E1⁄2FðŶnÞ2 FðXðtnÞÞ is investigated, where X(tn) is the exact solution at the nth time step and Ŷn is the approximate solution that includes computer rounding error. It is shown that rounding error is inversely proportional to the square root of the step size. An extrapolation technique provides second-order accuracy, and is one way to increase accuracy while avoiding rounding error. Several computational results are given.
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