The Experts below are selected from a list of 582294 Experts worldwide ranked by ideXlab platform
George Em Karniadakis - One of the best experts on this subject based on the ideXlab platform.
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fractional spectral collocation methods for linear and nonlinear variable order fpdes
Journal of Computational Physics, 2015Co-Authors: Mohsen Zayernouri, George Em KarniadakisAbstract:While several high-order methods have been developed for fractional PDEs (FPDEs) with fixed order, there are no such methods for FPDEs with field-variable order. These Equations allow multiphysics simulations seamlessly, e.g. from diffusion to sub-diffusion or from wave dynamics transitioning to diffusion, by simply varying the fractional order as a function of space or Time. We develop an exponentially accurate fractional spectral collocation method for solving linear/nonlinear FPDEs with field-variable order. Following the spectral theory, developed in 1] for fractional Sturm-Liouville eigenproblems, we introduce a new family of interpolants, called left-/right-sided and central fractional Lagrange interpolants. We employ the fractional derivatives of (left-/right-sided) Riemann-Liouville and Riesz type and obtain the corresponding fractional differentiation matrices by collocating the field-variable fractional orders. We solve several FPDEs including Time- and space-fractional advection-Equation, Time- and space-fractional advection-diffusion Equation, and finally the space-fractional Burgers' Equation to demonstrate the performance of the method. In addition, we develop a spectral penalty method for enforcing inhomogeneous initial conditions. Our numerical results confirm the exponential-like convergence of the proposed fractional collocation methods.
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fractional spectral collocation method
SIAM Journal on Scientific Computing, 2014Co-Authors: Mohsen Zayernouri, George Em KarniadakisAbstract:We develop an exponentially accurate fractional spectral collocation method for solving steady-state and Time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri and G. E. Karniadakis, J. Comput. Phys., 47 (2013), pp. 2108--2131] for fractional Sturm--Liouville eigenproblems. Subsequently, we obtain the corresponding fractional differentiation matrices, and we solve a number of linear FODEs in addition to linear and nonlinear FPDEs to investigate the numerical performance of the fractional collocation method. We first examine space-fractional advection-diffusion problem and generalized space-fractional multiterm FODEs. Next, we solve FPDEs, including the Time- and space-fractional advection-diffusion Equation, Time- and space-fractional multiterm FPDEs, and finally the space...
Mohsen Zayernouri - One of the best experts on this subject based on the ideXlab platform.
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fractional spectral collocation methods for linear and nonlinear variable order fpdes
Journal of Computational Physics, 2015Co-Authors: Mohsen Zayernouri, George Em KarniadakisAbstract:While several high-order methods have been developed for fractional PDEs (FPDEs) with fixed order, there are no such methods for FPDEs with field-variable order. These Equations allow multiphysics simulations seamlessly, e.g. from diffusion to sub-diffusion or from wave dynamics transitioning to diffusion, by simply varying the fractional order as a function of space or Time. We develop an exponentially accurate fractional spectral collocation method for solving linear/nonlinear FPDEs with field-variable order. Following the spectral theory, developed in 1] for fractional Sturm-Liouville eigenproblems, we introduce a new family of interpolants, called left-/right-sided and central fractional Lagrange interpolants. We employ the fractional derivatives of (left-/right-sided) Riemann-Liouville and Riesz type and obtain the corresponding fractional differentiation matrices by collocating the field-variable fractional orders. We solve several FPDEs including Time- and space-fractional advection-Equation, Time- and space-fractional advection-diffusion Equation, and finally the space-fractional Burgers' Equation to demonstrate the performance of the method. In addition, we develop a spectral penalty method for enforcing inhomogeneous initial conditions. Our numerical results confirm the exponential-like convergence of the proposed fractional collocation methods.
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fractional spectral collocation method
SIAM Journal on Scientific Computing, 2014Co-Authors: Mohsen Zayernouri, George Em KarniadakisAbstract:We develop an exponentially accurate fractional spectral collocation method for solving steady-state and Time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri and G. E. Karniadakis, J. Comput. Phys., 47 (2013), pp. 2108--2131] for fractional Sturm--Liouville eigenproblems. Subsequently, we obtain the corresponding fractional differentiation matrices, and we solve a number of linear FODEs in addition to linear and nonlinear FPDEs to investigate the numerical performance of the fractional collocation method. We first examine space-fractional advection-diffusion problem and generalized space-fractional multiterm FODEs. Next, we solve FPDEs, including the Time- and space-fractional advection-diffusion Equation, Time- and space-fractional multiterm FPDEs, and finally the space...
Zili Li - One of the best experts on this subject based on the ideXlab platform.
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forecasting day ahead electricity load using a multiple Equation Time series approach
European Journal of Operational Research, 2016Co-Authors: Adam Clements, A S Hurn, Zili LiAbstract:The quality of short-term electricity load forecasting is crucial to the operation and trading activities of market participants in an electricity market. In this paper, it is shown that a multiple Equation Time-series model, which is estimated by repeated application of ordinary least squares, has the potential to match or even outperform more complex nonlinear and nonparametric forecasting models. The key ingredient of the success of this simple model is the effective use of lagged information by allowing for interaction between seasonal patterns and intra-day dependencies. Although the model is built using data for the Queensland region of Australia, the method is completely generic and applicable to any load forecasting problem. The model’s forecasting ability is assessed by means of the mean absolute percentage error (MAPE). For day-ahead forecast, the MAPE returned by the model over a period of 11 years is an impressive 1.36%. The forecast accuracy of the model is compared with a number of benchmarks including three popular alternatives and one industrial standard reported by the Australia Energy Market Operator (AEMO). The performance of the model developed in this paper is superior to all benchmarks and outperforms the AEMO forecasts by about a third in terms of the MAPE criterion.
John R Freeman - One of the best experts on this subject based on the ideXlab platform.
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advances in bayesian Time series modeling and the study of politics theory testing forecasting and policy analysis
Political Analysis, 2006Co-Authors: Patrick T Brandt, John R FreemanAbstract:Bayesian approaches to the study of politics are increasingly popular. But Bayesian approaches to modeling multiple Time series have not been critically evaluated. This is in spite of the potential value of these models in international relations, political economy, and other fields of our discipline. We review recent developments in Bayesian multi-Equation Time series modeling in theory testing, forecasting, and policy analysis. Methods for constructing Bayesian measures of uncertainty of impulse responses (Bayesian shape error bands) are explained. A reference prior for these models that has proven useful in short- and medium-term forecasting in macroeconomics is described. Once modified to incorporate our experience analyzing political data and our theories, this prior can enhance our ability to forecast over the short and medium terms complex political dynamics like those exhibited by certain international conflicts. In addition, we explain how contingent Bayesian forecasts can be constructed, contingent Bayesian forecasts that embody policy counterfactuals. The value of these new Bayesian methods is illustrated in a reanalysis of the Israeli-Palestinian conflict of the 1980s.
Adam Clements - One of the best experts on this subject based on the ideXlab platform.
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forecasting day ahead electricity load using a multiple Equation Time series approach
European Journal of Operational Research, 2016Co-Authors: Adam Clements, A S Hurn, Zili LiAbstract:The quality of short-term electricity load forecasting is crucial to the operation and trading activities of market participants in an electricity market. In this paper, it is shown that a multiple Equation Time-series model, which is estimated by repeated application of ordinary least squares, has the potential to match or even outperform more complex nonlinear and nonparametric forecasting models. The key ingredient of the success of this simple model is the effective use of lagged information by allowing for interaction between seasonal patterns and intra-day dependencies. Although the model is built using data for the Queensland region of Australia, the method is completely generic and applicable to any load forecasting problem. The model’s forecasting ability is assessed by means of the mean absolute percentage error (MAPE). For day-ahead forecast, the MAPE returned by the model over a period of 11 years is an impressive 1.36%. The forecast accuracy of the model is compared with a number of benchmarks including three popular alternatives and one industrial standard reported by the Australia Energy Market Operator (AEMO). The performance of the model developed in this paper is superior to all benchmarks and outperforms the AEMO forecasts by about a third in terms of the MAPE criterion.