To study the heat or diffusion equation it is often used the Crank-Nicolson method which is unconditionally stable and has order of convergence O(k + h ), where k and h are mesh con2 2 stants. Unfortunately, using this method in conventional floatingpoint arithmetic we get solutions including not only the method error, but also representation and rounding error, Therefore, we propose an interva...

There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y(x) = f(x, y) starting from an initial value y0 = y(x0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a compu...

The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...

This paper develops a generalized framework for hedonic estimation that exploits experimental and quasi-experimental designs to relax many assumptions required by previous approaches. In the context of an idealized experiment, the identifiability is established of the distribution across consumers of the Marginal Willingness to Pay (MWTP) for a given product-specific amenity with few restrictio...

F with fragmented markets, saturated and demanding customers, and global competition, firms increasingly must design and offer a line of innovative, quality-differentiated products to target customers with differing willingness to pay (WTP). In this context, designing a special class of products that we term developmentintensive products (DIPs)—for which the fixed costs of development far outwe...

Compound real options are combinations of real options, where an exercise of a real option opens another real option. Compound real options are commonly found in a number of industrial projects, but are especially relevant in, e.g., research and development (R&D) where the R&D projects give the real option to research further, or to start the implementation of the results. Valuation of compound...

Within the last decades an increasing number of people practice risky sports in their leisure time. Although there exists a vast number of economic literature on risk-taking behavior, an estimation of the individual willingness to pay (WTP) for the option to exercise risk-taking is missing. Monetarized values could support private industries in design pricing schemes that set incentives to redu...

In various applications, computers are required to compute approximations to univariate elementary and special functions such as exp and arctan to modest accuracy. This paper proposes a new heuristic for automating the design of such implementations. This heuristic takes a certain restricted specification of program structure and the desired error properties as input and takes explicit account ...

An iterative algorithm is constructed to solve the linear matrix equation pair AXB E, CXD F over generalized reflexive matrix X. When the matrix equation pair AXB E, CXD F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the ...

The present investigation is concerned with estimating the rounding error in numerical solution of stochastic differential equations. A statistical rounding error analysis of Euler’s method for stochastic differential equations is performed. In particular, numerical evaluation of the quantities EjXðtnÞ2 Ŷnj and E1⁄2FðŶnÞ2 FðXðtnÞÞ is investigated, where X(tn) is the exact solution at the nth ti...