A method of piecewise-smooth numerical branching

A Method of Piecewise-Smooth Numerical Branching

A verified method for solving piecewise smooth initial value problems

In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is r...

Numerical method for optimal stopping of piecewise deterministic Markov processes

We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location – inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm an...

A Note on the Numerical Solution of the Wave Equation With Piecewise Smooth Coefficients

The numerical solution of the initial value problem for the wave equation is considered for the case when the equation coefficients are piecewise smooth. This problem models linear wave propagation in a medium in which the properties of the medium change discontinuously at interfaces. Convergent difference approximations can be found that do not require the explicit specification of the boundar...

Approximating Piecewise-Smooth Functions

We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate non-smooth functions. In such a case one usually expects the rate of approximation to be lower than that of smooth functions. It is shown in this paper that prior knowledge of the type of ’singularity’ of the function can be used to regain the full approximation power of the ...