Search

In this paper, we introduce a new method based on a library of chemical reactions for constructing a system of ordinary differential equations from stochastic simulations arising from an agent-based model. The advantage of this approach is that this library respects any coupling between systems components, whereas the SINDy algorithm (introduced by Brunton et al.) treats the individual components as decoupled from one another. Another advantage of our approach is that we can use a non-negative least squares algorithm to find the non-negative rate constants in a very robust, stable and simple manner. We illustrate our ideas on an agent-based model of tumour growth on a 2D lattice. [ABSTRACT FROM AUTHOR]

In order to construct an algorithm for homogeneous diffusive motion that lives on a sphere, we consider the equivalent process of a randomly rotating spin vector of constant length. By introducing appropriate sets of random variables based on cross products, we construct families of methods with increasing efficacy that exactly preserve the spin modulus for every realisation. This is done by exponentiating an antisymmetric matrix whose entries are these random variables that are Gaussian in the simplest case. [ABSTRACT FROM AUTHOR]

There has been considerable recent work on the development of energy conserving one-step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian, but care has to be taken in how the Wiener increments are sampled at each timestep. Some numerical simulations illustrate the performance of these methods. [ABSTRACT FROM AUTHOR]

In this paper, a class of new Magnus-type methods is proposed for non-commutative Itô stochastic differential equations (SDEs) with semi-linear drift term and semi-linear diffusion terms, based on Magnus expansion for non-commutative linear SDEs. We construct a Magnus-type Euler method, a Magnus-type Milstein method and a Magnus-type Derivative-free method, and give the mean-square convergence analysis of these methods. Numerical tests are carried out to present the efficiency of the proposed methods compared with the corresponding underlying methods and the specific performance of the simulation Itô integral algorithms is investigated. [ABSTRACT FROM AUTHOR]