We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity matrix of the process and obtain uniform (in time) error bounds of truncations. Our approach also guarantees that we can find limiting characteristics approximately with an arbitrarily fixed error. As an example, we obtain the respective bo...

One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of which Poisson is a special limiting case) approximation, so as to match the two supports of both distributions, and show that this will lead to improvements ...

The unusual implementation of explicit Falkner methods for solving special second-order initial-value problems increases the order of the method as will be shown by means of numerical examples. In this paper we made an analysis of the propagation of the truncation errors in both the usual and the unusual implementations, thus justifying the numerical results obtained. By that, some error bounds...

Two different linearized schemes are applied to a parametric finite-difference scheme concerning the numerical solution of the Boussinesq equation. At the first linearized scheme the nonlinear term of the equation is substituted by an appropriate value, while at the second scheme we use Taylor’s expansion. Both schemes are analyzed for local truncation error, stability and convergence. The resu...

Among the central concerns in mathematical finance is the evaluation of American options. An American option gives the holder the right but not the obligation to buy or sell a certain financial asset within a certain time-frame, for a certain strike price. The valuation of American options is formulated as an optimal stopping problem. If the stock price is modelled by a geometric Brownian motio...

A combined compact difference scheme is proposed for linear second-order partial differential equations with mixed derivative. The scheme is based on a nine-point stencil at interior with sixth-order accurate local truncation error. Fourier analysis is used to analyze the spectral resolution of the proposed scheme. Numerical tests demonstrate at least sixth-order convergence rate with Dirichlet...

In this article, we report an implicit rational method for solution of second order initial value problems in ordinary differential equation. We have presented local truncation error and stability property for the proposed method. We observed that the method has cubic rate of convergenceandA-stable. Numerical results for linear and nonlinear problems presented. These results confirm the accurac...

In this paper, we investigate a generalization of the Adams-Bashforth method by using the Taylor’s series. In case of m-step method, the local truncation error can be expressed in terms of m − 1 coefficients. With an appropriate choice of coefficients, the proposed method has produced much smaller error than the original Adams-Bashforth method. As an application of the generalized Adams-Bashfor...

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted L space. To obtain the schemes this expansion is terminated after P + 1 terms. We study the local truncation error and its behavior with respect to the step-size h and P . Building on this analysis, we develop an error ind...

In this paper the use of frequency-matched linear numerical integration techniques for the simulation of systems modelled by the dynamic phasors approach (DPA) is proposed and investigated. Such methods show an increased accuracy and computational efficiency around the matched frequency. Such frequency matched methods are derived by analyzing the local truncation error in the frequency domain a...