American options are priced numerically using a spaceand timeadaptive finite difference method. The generalized Black-Scholes operator is discretized on a Cartesian structured but non-equidistant grid in space. The spaceand time-discretizations are adjusted such that a predefined tolerance level on the local discretization error is met. An operator splitting technique is used to separately hand...

New pneumatic actuators developed in the author's laboratory will be presented with their applications to new mechatronics. Examples of them are a pneumatic rubber actuator for compliant robots, a micro pneumatic tube actuator assisting the colonscope insertion, a pneumatic stepping motor with high torque and resolution, a pneumatic drive bicycle, an intelligent pneumatic cylinder which has enc...

This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, ea...

This study was aimed at examining the gender and age-related differences of dynamic balance based on four stepping tests for the elderly. One hundred and eleven healthy subjects aged 60-85 were classified into four age groups (60-64, 65-69, 70-74, and 75-85) to examine age-related differences. They conducted stepping motions lasting 20-sec, including both-leg stepping right/left, both-leg stepp...

1 I n t r o d u c t i o n . This work appl ies some l inear a lgebra ideas in an o rd ina ry differential equa t ion (ODE) context . We begin by summar i s ing the a p p r o p r i a t e l inear a lgebra , and then we in t roduce the O D E problem. *Received July 1995. Revised July 1996. tThis work was supported by Engineering and Physical Sciences Research Council grants GR/H94634 and GR/KS0228...

This report introduces the “Time Stepping Package for Optimization”, or TSOpt, which is an interface for time-stepping simulation written in C++. It packages a simulator together with its derivatives (“sensitivities”) and adjoint derivatives with respect to simulation parameters in a single object called a Jet, which can be used in conjunction with an optimization algorithm to solve a simulatio...

In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the ...

In this abstract, we present a case study in the application of a time-stepping method, unconstrained by the CFL condition, for computational acoustic wave propagation in the context of full waveform inversion. The numerical scheme is a locally one-dimensional (LOD) variant of alternating dimension implicit (ADI) method. The LOD method has a maximum time step that is restricted only by the Nyqu...

In this work, we will analyze a class of large time-stepping methods for the Cahn–Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerica...