Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) with a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus, but since the driving stochastic process is usually only Hölder continuous in time, the vector field is not differentiable in the time variable, so traditional numerical schemes for ODEs do not achi...

We use a stochastic approach to show how Taylor dispersion is affected by kinetic processes of adsorption and desorption onto surfaces. A general theory is developed, from which we derive explicitly the dispersion coefficients of canonical examples such as Poiseuille flows in planar and cylindrical geometries, in both constant and sinusoidal velocity fields. These results open the way for the m...

A notion of the heat kernel measure is introduced for the L2 completion of a hyperfinite II1-factor with respect to the trace. Some properties of this measure are derived from the corresponding stochastic differential equation. Then the Taylor map is studied for a space of holomorphic functions square integrable with respect to the heat kernel measure. We also define a skeleton map from this sp...

The standard method for stochastic representation of the fermion determinant is the pseudofermion method [1]. It allows to trade the computation of the determinant in favour of extra noise in the path integral of lattice QCD. The other alternative is to use the stochastic Taylor expansion of [2]. This suffers from the so called probability sign problem which is created by the noise [3]. The pro...

In this paper, it is revealed that Adomian decomposition method corresponds to Taylor series method when applied to the solution of nonlinear initial value problems, in the following sense: the Adomian ́s polynomials can be obtain trough Taylor coefficients.

The article is devoted to optimization of the mean-square approximation procedures for iterated Ito stochastic integrals multiplicities 1 5. mentioned are part strong numerical methods with convergence orders 1.0, 1.5, 2.0, and 2.5 differential equations multidimensional non-commutative noise based on unified Taylor-Ito expansion multiple Fourier-Legendre series converging in sense norm Hilbert...

We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Equations with terminal conditions that time-steps the BSDE backwards and apply it to differential rates problem as prototypical nonlinear of independent financial interest. The equation backward time-step is solved exactly or by Taylor-based approximation. This first application such time-stepping ap...

Universit .2012.07.0 Abstract A Taylor collocation method has been developed to solve the systems of high-order linear differential–difference equations in terms of the Taylor polynomials. Using the Taylor collocation points, this method transforms differential–difference equation systems and the given conditions to matrix equations with unknown Taylor coefficients. By means of the obtained mat...

The aim of this paper is to apply the Taylor expansion method solve first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: FPA DSA. In order DSA, we use CESTAC CADNA library. Using method, can find optimal step approximation, error, some numerical instabilities. They are novelties DSA in comparison FPA. error analysis proved. Furthermore...

In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method. In the present paper, we demonstrate that such a view is only valid in very special cases, and in general the homotopy analysis method is far more robust. In particular...