Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method

An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix ordinary differential equations. Next, VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method's higher numerical stability and precision

Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation

Metzler et al. introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a Boltzmann thermal heat bath. In this paper, we present an interval Shannon wavelet numerical method for the FFPE. In this method, a new concept named “dynamic interval wavelet” is proposed to solve the problem that the numerical solution of the fractional PDE is usually sensitive to boundary conditions. Comparing with the traditional wavelet defined in the interval, the Newton interpolator is employed instead of the Lagrange interpolation operator, so, the extrapolation points in the interval wavelet can be chosen dynamically to restrict the boundary effect without increase of the calculation amount. In order to avoid unlimited increasing of the extrapolation points, both the error tolerance and the condition number are taken as indicators for the dynamic choice of the extrapolation points. Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed. A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA)

Monitoring and modelling hydrological response and sediment yield in a North York Moors catchment : an assessment of predictive uncertainty in a coupled hydrological-sediment yield model

A fully distributed coupled hydrological-sediment yield model was developed. An assessment was made of the predictive uncertainty in the individual model predictions, as well as the uncertainty propagated from the primary hydrological model to the secondary sediment yield model, using the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. The value of additional data, in the form of additional periods of flow data, as well as deterministic (based on landuse and soil type) and random spatial parameterisation of hydrological parameters in restricting model uncertainty of the spatially lumped model parameterisation were examined, using Bayesian updating.The results revealed significant model uncertainty in both the hydrological and sediment yield models, with uncertainty bounds widest at peak flow and sediment flux, and predictive failure in recession flows, similar to other applications of GLUE methodology. Uncertainty in the sediment yield model was found to be due to uncertainty inherited from the hydrological model, as well as simplifying assumptions made about sediment removal and transport, and resulted in lower model efficiencies and generally poorer qualitative sedigraph fit.The model validation exercise revealed that the calibrated 'optimum' parameter set was not 'optimum' for all validation periods and resulted in inaccurate spatial and temporal hydrological response predictions for the validation periods. This suggested that traditional split-sample model calibration methods may not be effective in capturing the true spatial and temporal variability of the system.Successive periods of flow data were effective in reducing the calibration period uncertainty bounds. Similarly, the use of sediment yield predictions to update hydrological model uncertainty resulted in a reduction in hydrological model uncertainty. Spatially distributed parameterisation was found to also improve model predictions, resulting in a reduction in uncertainty bounds, particularly for soil-distributed parameterisation. However, stochastic parameterisation of spatially variable hydrological parameters provided equally acceptable predictions for both models, suggesting that a deterministic approach might not be required to capture the spatial variability in hydrological and sedimentological response in the study catchment, and that a stochastic approach may be adequate

Monitoring and modelling hydrological response and sediment yield in a North York Moors catchment : an assessment of predictive uncertainty in a coupled hydrological-sediment yield model

A fully distributed coupled hydrological-sediment yield model was developed. An assessment was made of the predictive uncertainty in the individual model predictions, as well as the uncertainty propagated from the primary hydrological model to the secondary sediment yield model, using the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. The value of additional data, in the form of additional periods of flow data, as well as deterministic (based on landuse and soil type) and random spatial parameterisation of hydrological parameters in restricting model uncertainty of the spatially lumped model parameterisation were examined, using Bayesian updating.The results revealed significant model uncertainty in both the hydrological and sediment yield models, with uncertainty bounds widest at peak flow and sediment flux, and predictive failure in recession flows, similar to other applications of GLUE methodology. Uncertainty in the sediment yield model was found to be due to uncertainty inherited from the hydrological model, as well as simplifying assumptions made about sediment removal and transport, and resulted in lower model efficiencies and generally poorer qualitative sedigraph fit.The model validation exercise revealed that the calibrated 'optimum' parameter set was not 'optimum' for all validation periods and resulted in inaccurate spatial and temporal hydrological response predictions for the validation periods. This suggested that traditional split-sample model calibration methods may not be effective in capturing the true spatial and temporal variability of the system.Successive periods of flow data were effective in reducing the calibration period uncertainty bounds. Similarly, the use of sediment yield predictions to update hydrological model uncertainty resulted in a reduction in hydrological model uncertainty. Spatially distributed parameterisation was found to also improve model predictions, resulting in a reduction in uncertainty bounds, particularly for soil-distributed parameterisation. However, stochastic parameterisation of spatially variable hydrological parameters provided equally acceptable predictions for both models, suggesting that a deterministic approach might not be required to capture the spatial variability in hydrological and sedimentological response in the study catchment, and that a stochastic approach may be adequate

Aeronautical Engineering: A continuing bibliography with indexes, supplement 97

This bibliography lists 420 reports, articles, and other documents introduced into the NASA scientific and technical information system in May 1978

Predicting malaria dynamics under climate change

Malaria dynamics are closely tied to climate, as rainfed water pools provide the habitat for the Anopheles mosquitoes, and temperature influences this vector's ability to spread disease. Climate change drives shifts in microtopographic controls on the persistence of mosquito habitat and the life cycles of Anopheles vector and Plasmodium parasite, which affect the transmission of malaria. The ability to accurately predict malaria dynamics in the future requires the consideration of the impacts of modifications in ecohydrologic system under climate change on these shifts. The primary goal of this research is to investigate the relationships between the dynamics of malaria and changes in the ecohydrologic system due to the acclimation of vegetation under elevated atmospheric CO2 condition and temperature increase. We also aim to understand how the dominant controls of malaria interact under environmental perturbations by quantitatively analyzing changes in malaria incidence rates. Here, a coupled ecohydrology-malaria dynamics model is developed to predict malaria dynamics under projected climate change. The impacts of ecologic acclimation on soil moisture and persistence of ponded water that provide habitat for mosquitoes are captured using a coupled multi-layer canopy and physically-based flow surface-subsurface modeling approach. The transmission of malaria in response to these impacts and temperature increase are assessed by using a stochastic meta-popolation simulation model. We show that impacts of elevated CO2 and temperature have opposing effects on malaria prevalence. While air temperature increase shortens the life cycles of Anopheles and Plasmodium and increases the risk of spreading the disease, lower soil moisture resulting from increasing evapotranspiration reduces the habitat suitability for mosquitoes. The interplay between air temperature increases and soil moisture reduction under climate change leads to a smaller net increase in environmental suitability for malaria transmission than previously thought. In addition, we found larger net increase of malaria incidence under high temperature increase due to its nonlinear effects on the life cycles of vectors and parasites. The models and methods used are generalized and can be applied to other mosquito-borne diseases

Proceedings of the XXIIIrd TELEMAC-MASCARET User Conference 2016, 11 to 13 October 2016, Paris, France

Water Qualit