6 research outputs found
Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations
We propose new explicit exponential Runge-Kutta methods for the weak approximation of solutions of stiff ItĂ´ stochastic differential equations (SDEs). We also consider the use of exponential Runge-Kutta methods in combination with splitting methods. These methods have weak order 2 for multidimensional, noncommutative SDEs with a semilinear drift term, whereas they are of order 2 or 3 for semilinear ordinary differential equations. These methods are A-stable in the mean square sense for a scalar linear test equation whose drift and diffusion terms have complex coefficients. We carry out numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order 2
Exponential Integrators for Stochastic Maxwell's Equations Driven by It\^o Noise
This article presents explicit exponential integrators for stochastic
Maxwell's equations driven by both multiplicative and additive noises. By
utilizing the regularity estimate of the mild solution, we first prove that the
strong order of the numerical approximation is for general
multiplicative noise. Combing a proper decomposition with the stochastic
Fubini's theorem, the strong order of the proposed scheme is shown to be
for additive noise. Moreover, for linear stochastic Maxwell's equation with
additive noise, the proposed time integrator is shown to preserve exactly the
symplectic structure, the evolution of the energy as well as the evolution of
the divergence in the sense of expectation. Several numerical experiments are
presented in order to verify our theoretical findings.Comment: 21 Page
Weak second order explicit exponential RUNGE-KUTTA methods for stochastic differential equations
We propose new explicit exponential Runge–Kutta methods for the weak approximation of solutions of stiff It\uf4 stochastic differential equations (SDEs). We also consider the use of exponential Runge–Kutta methods in combination with splitting methods. These methods have weak order 2 for multidimensional, noncommutative SDEs with a semilinear drift term, whereas they are of order 2 or 3 for semilinear ordinary differential equations. These methods are A-stable in the mean square sense for a scalar linear test equation whose drift and diffusion terms have complex coefficients. We carry out numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order 2