A collocation method based on modified cubic B-spline functions has been developed for the valuation of European, American and barrier options of a single asset. The new approach contains discretization of temporal derivative using finite difference approximation of and approximating the option price with the modified B-spline functions. Stability of this method has been discussed and it is sho...

The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton–Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gr...

The modified log-wake law, which was developed for turbulent boundary layers and pipe flows, is extended to turbulent flows in open-channels. Turbulent velocity profiles in open-channels can be approximated with three components: (1) the law of the wall that results from the constant bed shear stress; (2) the law of the wake that reflects the effects of gravity, secondary currents and bed rough...