The aim of the article is to demonstrate the use of the Laplace transform to the evaluation of consols’ present value under different streams of returns (dividends). Consols (or perpetual bonds, perpetuities) are bonds with no maturity, which means that interest is paid to a bondholder perpetually (usually annually) forever. The present value of a consol, when constant interest is paid, is simp...

Conservative numerical schemes for general relativistic magnetohydrodynamics (GRMHD) require a method for transforming between “conserved” variables such as momentum and energy density and “primitive” variables such as restmass density, internal energy, and components of the four-velocity. The forward transformation (primitive to conserved) has a closed-form solution, but the inverse transforma...

For scalar, electromagnetic, or gravitational wave propagation on a background Schwarzschild blackhole, we describe the exact nonlocal radiation outer boundary conditions (robc) appropriate for a spherical outer boundary of finite radius enclosing the blackhole. Derivation of the robc is based on Laplace and spherical– harmonic transformation of the Regge–Wheeler equation, the pde governing the...

Methods for the numerical inversion of a Laplace transform F(s) which use a special bilinear transformation of s are particularly eeective in many cases and are widely used. The main purpose of this paper is to analyze the convergence and conditioning properties of a special class of such methods, characterized by the use of Lagrange interpolation. The results derived apply both to complex and ...