Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
The Journal of Supercomputing - Special issue on supercomputing in medicine
Molecular Modeling and Simulation: An Interdisciplinary Guide
Molecular Modeling and Simulation: An Interdisciplinary Guide
A computational model of flow through porous media at the microscale
A computational model of flow through porous media at the microscale
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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A stochastic numerical scheme for an extended immersed boundary method which incorporates thermal fluctuations for the simulation of microscopic biological systems consisting of fluid and immersed elastica was introduced in reference [2]. The numerical scheme uses techniques from stochastic calculus to overcome stability and accuracy issues associated with standard finite difference methods. The numerical scheme handles a range of time steps in a unified manner, including time steps which are greater than the smallest time scales of the system. The time step regimes we shall investigate can be classified as small, intermediate, or large relative to the time scales of the fluid dynamics of the system. Small time steps resolve in a computationally explicit manner the dynamics of all the degrees of freedom of the system. Large time steps resolve in a computationally explicit manner only the degrees of freedom of the immersed elastica, with the contributions of the dynamics of the fluid degrees of freedom accounted for in only a statistical manner over a time step. Intermediate time steps resolve in a computationally explicit manner only some degrees of freedom of the fluid with the remaining degrees of freedom accounted for statistically over a time step. In this paper, uniform bounds are established for the strong error of the stochastic numerical method for each of the time step regimes. The scaling of the numerical errors with respect to the parameters of the method is then discussed.